Suppose we are considering the question of how much capacity to build in the face of uncertain demand. Assume that the cost is $20 per unit of lost sales due to insufficient capacity, Also assume that there is a cost of $7 for each unit of capacity built. The probability of various demand levels is as follows: Deman d- X Units Probability of X 0 .05 1 .10 2 .15 3 .20 4 .20 5 .15 6 .10 7 .05 a. How many units of capacity should be built to minimize the total cost of providing capacity plus lost sales? b. State a general rule regarding the amount of capacity to build. c. What principle does this problem illustrate?

Question

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Answer 1

Textbook Question

Chapter 11, Problem 1P

Suppose we are considering the question of how much capacity to build in the face of uncertain demand. Assume that the cost is $20 per unit of lost sales due to insufficient capacity, Also assume that there is a cost of $7 for each unit of capacity built. The probability of various demand levels is as follows:

Deman d- X Units	Probability of X
0	.05
1	.10
2	.15
3	.20
4	.20
5	.15
6	.10
7	.05

a. How many units of capacity should be built to minimize the total cost of providing capacity plus lost sales?
b. State a general rule regarding the amount of capacity to build.
c. What principle does this problem illustrate?

a)

Expert Solution

Summary Introduction

To determine: The number of capacity units required to minimize the total cost of providing capacity plus lost sales.

Introduction:

Capacity planning is the process of planning the required production output based on the requirement or the demand that is predicted.

Explanation of Solution

Given information:

It is given that the cost of the lost sales is $20 per unit, due to insufficient capacity. Assume that the cost is $7 for each unit of capacity built. In addition to this, the following information is given:

Demand - X units	Probability of X
0	0.05
1	0.10
2	0.15
3	0.20
4	0.20
5	0.15
6	0.10
7	0.05

Build 0 units of capacity:

It is calculated by adding capacity cost and penalty cost.

Build 0 units of capacity=(7×0)+20[(0×0.05)+(1×0.10)+(2×0.15)+(3×0.20)+(4×0.20)+(5×0.15)+(6×0.10)+(7×0.05)]=0+20(0+0.10+0.30+0.60+0.80+0.75+0.60+0.35)=20×3.5=70

Build 1 unit of capacity:

It is calculated by adding capacity cost and penalty cost.

Build 1 unit of capacity=(7×1)+20[(0×(0.05+0.10))+(1×0.15)+(2×0.2)+(3×0.20)+(4×0.15)+(5×0.10)+(6×0.05)]=7+20(0+0.15+0.40+0.60+0.60+0.50+0.30)=7+(20×2.55)=58

Build 2 units of capacity:

It is calculated by adding capacity cost and penalty cost.

Build 2 units of capacity=(7×2)+20[(0×(0.05+0.10+0.15))+(1×0.20)+(2×0.2)+(3×0.15)+(4×0.10)+(5×0.05)]=14+20(0+0.20+0.40+0.45+0.40+0.25)=14+(20×1.7)=48

Build 3 units of capacity:

It is calculated by adding capacity cost and penalty cost.

Build 3 units of capacity=(7×3)+20[(0×(0.05+0.10+0.15+0.20))+(1×0.20)+(2×0.15)+(3×0.10)+(4×0.05)]=21+20(0+0.20+0.30+0.30+0.20)=21+(20×1)=41

Build 4 units of capacity:

It is calculated by adding capacity cost and penalty cost.

Build 4 units of capacity=(7×4)+20[(0×(0.05+0.10+0.15+0.20+0.20))+(1×0.15)+(2×0.10)+(3×0.05)]=28+20(0+0.15+0.20+0.15)=28+(20×0.50)=38

Build 5 units of capacity:

It is calculated by adding capacity cost and penalty cost.

Build 5 units of capacity=(7×5)+20[(0×(0.05+0.10+0.15+0.20+0.20+0.15))+(1×0.10)+(2×0.05)]=35+20(0+0.10+0.10)=35+(20×0.20)=39

Build 6 units of capacity:

It is calculated by adding capacity cost and penalty cost.

Build 6 units of capacity=(7×6)+20[(0×(0.05+0.10+0.15+0.20+0.20+0.15+0.10))+(1×0.05)]=42+20(0+0.05)=42+(20×0.05)=43

Build 7 units of capacity:

It is calculated by adding capacity cost and penalty cost.

Build 7 units of capacity=(7×7)+20[(0×(0.05+0.10+0.15+0.20+0.20+0.15+0.10+0.05))]=49+20(0)=49

Hence, the number of capacity units required (that has the minimum total cost of $38) to minimize the total cost of providing capacity plus lost sales is 4 units.

b)

Expert Solution

Summary Introduction

To determine: The general rule regarding the amount of capacity to build.

Introduction:

Capacity planning is the process of planning the required production output based on the requirement or the demand that is predicted.

Explanation of Solution

Given information:

It is given that the cost of the lost sales is $20 per unit due to insufficient capacity. Assume that the cost is $7 for each unit of capacity built. In addition to this, the following information is given:

Demand - X units	Probability of X
0	0.05
1	0.10
2	0.15
3	0.20
4	0.20
5	0.15
6	0.10
7	0.05

General instruction regarding the amount of capacity to build:

The general instruction regarding the amount of capacity to build is to minimize the total cost of capacity plus lost sales.

c)

Expert Solution

Summary Introduction

To determine: The principle that is illustrated in the problem.

Introduction:

Capacity planning is the process of planning the required production output based on the requirement or the demand that is predicted.

Explanation of Solution

Given information:

It is given that the cost of the lost sales is $20 per unit due to insufficient capacity. Assume that the cost is $7 for each unit of capacity built. In addition to this, the following information is given:

Demand - X units	Probability of X
0	0.05
1	0.10
2	0.15
3	0.20
4	0.20
5	0.15
6	0.10
7	0.05

Determine the principle that is illustrated in the problem:

In the given problem, the trade-off between excess capacity and lost sales is illustrated.

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Answer 2

Textbook Question

Chapter 11, Problem 1P

Suppose we are considering the question of how much capacity to build in the face of uncertain demand. Assume that the cost is $20 per unit of lost sales due to insufficient capacity, Also assume that there is a cost of $7 for each unit of capacity built. The probability of various demand levels is as follows:

Deman d- X Units	Probability of X
0	.05
1	.10
2	.15
3	.20
4	.20
5	.15
6	.10
7	.05

a. How many units of capacity should be built to minimize the total cost of providing capacity plus lost sales?
b. State a general rule regarding the amount of capacity to build.
c. What principle does this problem illustrate?

a)

Expert Solution

Summary Introduction

To determine: The number of capacity units required to minimize the total cost of providing capacity plus lost sales.

Introduction:

Capacity planning is the process of planning the required production output based on the requirement or the demand that is predicted.

Explanation of Solution

Given information:

It is given that the cost of the lost sales is $20 per unit, due to insufficient capacity. Assume that the cost is $7 for each unit of capacity built. In addition to this, the following information is given:

Demand - X units	Probability of X
0	0.05
1	0.10
2	0.15
3	0.20
4	0.20
5	0.15
6	0.10
7	0.05

Build 0 units of capacity:

It is calculated by adding capacity cost and penalty cost.

Build 0 units of capacity=(7×0)+20[(0×0.05)+(1×0.10)+(2×0.15)+(3×0.20)+(4×0.20)+(5×0.15)+(6×0.10)+(7×0.05)]=0+20(0+0.10+0.30+0.60+0.80+0.75+0.60+0.35)=20×3.5=70

Build 1 unit of capacity:

It is calculated by adding capacity cost and penalty cost.

Build 1 unit of capacity=(7×1)+20[(0×(0.05+0.10))+(1×0.15)+(2×0.2)+(3×0.20)+(4×0.15)+(5×0.10)+(6×0.05)]=7+20(0+0.15+0.40+0.60+0.60+0.50+0.30)=7+(20×2.55)=58

Build 2 units of capacity:

It is calculated by adding capacity cost and penalty cost.

Build 2 units of capacity=(7×2)+20[(0×(0.05+0.10+0.15))+(1×0.20)+(2×0.2)+(3×0.15)+(4×0.10)+(5×0.05)]=14+20(0+0.20+0.40+0.45+0.40+0.25)=14+(20×1.7)=48

Build 3 units of capacity:

It is calculated by adding capacity cost and penalty cost.

Build 3 units of capacity=(7×3)+20[(0×(0.05+0.10+0.15+0.20))+(1×0.20)+(2×0.15)+(3×0.10)+(4×0.05)]=21+20(0+0.20+0.30+0.30+0.20)=21+(20×1)=41

Build 4 units of capacity:

It is calculated by adding capacity cost and penalty cost.

Build 4 units of capacity=(7×4)+20[(0×(0.05+0.10+0.15+0.20+0.20))+(1×0.15)+(2×0.10)+(3×0.05)]=28+20(0+0.15+0.20+0.15)=28+(20×0.50)=38

Build 5 units of capacity:

It is calculated by adding capacity cost and penalty cost.

Build 5 units of capacity=(7×5)+20[(0×(0.05+0.10+0.15+0.20+0.20+0.15))+(1×0.10)+(2×0.05)]=35+20(0+0.10+0.10)=35+(20×0.20)=39

Build 6 units of capacity:

It is calculated by adding capacity cost and penalty cost.

Build 6 units of capacity=(7×6)+20[(0×(0.05+0.10+0.15+0.20+0.20+0.15+0.10))+(1×0.05)]=42+20(0+0.05)=42+(20×0.05)=43

Build 7 units of capacity:

It is calculated by adding capacity cost and penalty cost.

Build 7 units of capacity=(7×7)+20[(0×(0.05+0.10+0.15+0.20+0.20+0.15+0.10+0.05))]=49+20(0)=49

Hence, the number of capacity units required (that has the minimum total cost of $38) to minimize the total cost of providing capacity plus lost sales is 4 units.

b)

Expert Solution

Summary Introduction

To determine: The general rule regarding the amount of capacity to build.

Introduction:

Capacity planning is the process of planning the required production output based on the requirement or the demand that is predicted.

Explanation of Solution

Given information:

It is given that the cost of the lost sales is $20 per unit due to insufficient capacity. Assume that the cost is $7 for each unit of capacity built. In addition to this, the following information is given:

Demand - X units	Probability of X
0	0.05
1	0.10
2	0.15
3	0.20
4	0.20
5	0.15
6	0.10
7	0.05

General instruction regarding the amount of capacity to build:

The general instruction regarding the amount of capacity to build is to minimize the total cost of capacity plus lost sales.

c)

Expert Solution

Summary Introduction

To determine: The principle that is illustrated in the problem.

Introduction:

Capacity planning is the process of planning the required production output based on the requirement or the demand that is predicted.

Explanation of Solution

Given information:

It is given that the cost of the lost sales is $20 per unit due to insufficient capacity. Assume that the cost is $7 for each unit of capacity built. In addition to this, the following information is given:

Demand - X units	Probability of X
0	0.05
1	0.10
2	0.15
3	0.20
4	0.20
5	0.15
6	0.10
7	0.05

Determine the principle that is illustrated in the problem:

In the given problem, the trade-off between excess capacity and lost sales is illustrated.

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 3

Textbook Question

Chapter 11, Problem 1P

Suppose we are considering the question of how much capacity to build in the face of uncertain demand. Assume that the cost is $20 per unit of lost sales due to insufficient capacity, Also assume that there is a cost of $7 for each unit of capacity built. The probability of various demand levels is as follows:

Deman d- X Units	Probability of X
0	.05
1	.10
2	.15
3	.20
4	.20
5	.15
6	.10
7	.05

a. How many units of capacity should be built to minimize the total cost of providing capacity plus lost sales?
b. State a general rule regarding the amount of capacity to build.
c. What principle does this problem illustrate?

a)

Expert Solution

Summary Introduction

To determine: The number of capacity units required to minimize the total cost of providing capacity plus lost sales.

Introduction:

Capacity planning is the process of planning the required production output based on the requirement or the demand that is predicted.

Explanation of Solution

Given information:

It is given that the cost of the lost sales is $20 per unit, due to insufficient capacity. Assume that the cost is $7 for each unit of capacity built. In addition to this, the following information is given:

Demand - X units	Probability of X
0	0.05
1	0.10
2	0.15
3	0.20
4	0.20
5	0.15
6	0.10
7	0.05

Build 0 units of capacity:

It is calculated by adding capacity cost and penalty cost.

Build 0 units of capacity=(7×0)+20[(0×0.05)+(1×0.10)+(2×0.15)+(3×0.20)+(4×0.20)+(5×0.15)+(6×0.10)+(7×0.05)]=0+20(0+0.10+0.30+0.60+0.80+0.75+0.60+0.35)=20×3.5=70

Build 1 unit of capacity:

It is calculated by adding capacity cost and penalty cost.

Build 1 unit of capacity=(7×1)+20[(0×(0.05+0.10))+(1×0.15)+(2×0.2)+(3×0.20)+(4×0.15)+(5×0.10)+(6×0.05)]=7+20(0+0.15+0.40+0.60+0.60+0.50+0.30)=7+(20×2.55)=58

Build 2 units of capacity:

It is calculated by adding capacity cost and penalty cost.

Build 2 units of capacity=(7×2)+20[(0×(0.05+0.10+0.15))+(1×0.20)+(2×0.2)+(3×0.15)+(4×0.10)+(5×0.05)]=14+20(0+0.20+0.40+0.45+0.40+0.25)=14+(20×1.7)=48

Build 3 units of capacity:

It is calculated by adding capacity cost and penalty cost.

Build 3 units of capacity=(7×3)+20[(0×(0.05+0.10+0.15+0.20))+(1×0.20)+(2×0.15)+(3×0.10)+(4×0.05)]=21+20(0+0.20+0.30+0.30+0.20)=21+(20×1)=41

Build 4 units of capacity:

It is calculated by adding capacity cost and penalty cost.

Build 4 units of capacity=(7×4)+20[(0×(0.05+0.10+0.15+0.20+0.20))+(1×0.15)+(2×0.10)+(3×0.05)]=28+20(0+0.15+0.20+0.15)=28+(20×0.50)=38

Build 5 units of capacity:

It is calculated by adding capacity cost and penalty cost.

Build 5 units of capacity=(7×5)+20[(0×(0.05+0.10+0.15+0.20+0.20+0.15))+(1×0.10)+(2×0.05)]=35+20(0+0.10+0.10)=35+(20×0.20)=39

Build 6 units of capacity:

It is calculated by adding capacity cost and penalty cost.

Build 6 units of capacity=(7×6)+20[(0×(0.05+0.10+0.15+0.20+0.20+0.15+0.10))+(1×0.05)]=42+20(0+0.05)=42+(20×0.05)=43

Build 7 units of capacity:

It is calculated by adding capacity cost and penalty cost.

Build 7 units of capacity=(7×7)+20[(0×(0.05+0.10+0.15+0.20+0.20+0.15+0.10+0.05))]=49+20(0)=49

Hence, the number of capacity units required (that has the minimum total cost of $38) to minimize the total cost of providing capacity plus lost sales is 4 units.

b)

Expert Solution

Summary Introduction

To determine: The general rule regarding the amount of capacity to build.

Introduction:

Capacity planning is the process of planning the required production output based on the requirement or the demand that is predicted.

Explanation of Solution

Given information:

It is given that the cost of the lost sales is $20 per unit due to insufficient capacity. Assume that the cost is $7 for each unit of capacity built. In addition to this, the following information is given:

Demand - X units	Probability of X
0	0.05
1	0.10
2	0.15
3	0.20
4	0.20
5	0.15
6	0.10
7	0.05

General instruction regarding the amount of capacity to build:

The general instruction regarding the amount of capacity to build is to minimize the total cost of capacity plus lost sales.

c)

Expert Solution

Summary Introduction

To determine: The principle that is illustrated in the problem.

Introduction:

Capacity planning is the process of planning the required production output based on the requirement or the demand that is predicted.

Explanation of Solution

Given information:

It is given that the cost of the lost sales is $20 per unit due to insufficient capacity. Assume that the cost is $7 for each unit of capacity built. In addition to this, the following information is given:

Demand - X units	Probability of X
0	0.05
1	0.10
2	0.15
3	0.20
4	0.20
5	0.15
6	0.10
7	0.05

Determine the principle that is illustrated in the problem:

In the given problem, the trade-off between excess capacity and lost sales is illustrated.

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 4

Textbook Question

Chapter 11, Problem 1P

Suppose we are considering the question of how much capacity to build in the face of uncertain demand. Assume that the cost is $20 per unit of lost sales due to insufficient capacity, Also assume that there is a cost of $7 for each unit of capacity built. The probability of various demand levels is as follows:

Deman d- X Units	Probability of X
0	.05
1	.10
2	.15
3	.20
4	.20
5	.15
6	.10
7	.05

a. How many units of capacity should be built to minimize the total cost of providing capacity plus lost sales?
b. State a general rule regarding the amount of capacity to build.
c. What principle does this problem illustrate?

a)

Expert Solution

Summary Introduction

To determine: The number of capacity units required to minimize the total cost of providing capacity plus lost sales.

Introduction:

Capacity planning is the process of planning the required production output based on the requirement or the demand that is predicted.

Explanation of Solution

Given information:

It is given that the cost of the lost sales is $20 per unit, due to insufficient capacity. Assume that the cost is $7 for each unit of capacity built. In addition to this, the following information is given:

Demand - X units	Probability of X
0	0.05
1	0.10
2	0.15
3	0.20
4	0.20
5	0.15
6	0.10
7	0.05

Build 0 units of capacity:

It is calculated by adding capacity cost and penalty cost.

Build 0 units of capacity=(7×0)+20[(0×0.05)+(1×0.10)+(2×0.15)+(3×0.20)+(4×0.20)+(5×0.15)+(6×0.10)+(7×0.05)]=0+20(0+0.10+0.30+0.60+0.80+0.75+0.60+0.35)=20×3.5=70

Build 1 unit of capacity:

It is calculated by adding capacity cost and penalty cost.

Build 1 unit of capacity=(7×1)+20[(0×(0.05+0.10))+(1×0.15)+(2×0.2)+(3×0.20)+(4×0.15)+(5×0.10)+(6×0.05)]=7+20(0+0.15+0.40+0.60+0.60+0.50+0.30)=7+(20×2.55)=58

Build 2 units of capacity:

It is calculated by adding capacity cost and penalty cost.

Build 2 units of capacity=(7×2)+20[(0×(0.05+0.10+0.15))+(1×0.20)+(2×0.2)+(3×0.15)+(4×0.10)+(5×0.05)]=14+20(0+0.20+0.40+0.45+0.40+0.25)=14+(20×1.7)=48

Build 3 units of capacity:

It is calculated by adding capacity cost and penalty cost.

Build 3 units of capacity=(7×3)+20[(0×(0.05+0.10+0.15+0.20))+(1×0.20)+(2×0.15)+(3×0.10)+(4×0.05)]=21+20(0+0.20+0.30+0.30+0.20)=21+(20×1)=41

Build 4 units of capacity:

It is calculated by adding capacity cost and penalty cost.

Build 4 units of capacity=(7×4)+20[(0×(0.05+0.10+0.15+0.20+0.20))+(1×0.15)+(2×0.10)+(3×0.05)]=28+20(0+0.15+0.20+0.15)=28+(20×0.50)=38

Build 5 units of capacity:

It is calculated by adding capacity cost and penalty cost.

Build 5 units of capacity=(7×5)+20[(0×(0.05+0.10+0.15+0.20+0.20+0.15))+(1×0.10)+(2×0.05)]=35+20(0+0.10+0.10)=35+(20×0.20)=39

Build 6 units of capacity:

It is calculated by adding capacity cost and penalty cost.

Build 6 units of capacity=(7×6)+20[(0×(0.05+0.10+0.15+0.20+0.20+0.15+0.10))+(1×0.05)]=42+20(0+0.05)=42+(20×0.05)=43

Build 7 units of capacity:

It is calculated by adding capacity cost and penalty cost.

Build 7 units of capacity=(7×7)+20[(0×(0.05+0.10+0.15+0.20+0.20+0.15+0.10+0.05))]=49+20(0)=49

Hence, the number of capacity units required (that has the minimum total cost of $38) to minimize the total cost of providing capacity plus lost sales is 4 units.

b)

Expert Solution

Summary Introduction

To determine: The general rule regarding the amount of capacity to build.

Introduction:

Capacity planning is the process of planning the required production output based on the requirement or the demand that is predicted.

Explanation of Solution

Given information:

It is given that the cost of the lost sales is $20 per unit due to insufficient capacity. Assume that the cost is $7 for each unit of capacity built. In addition to this, the following information is given:

Demand - X units	Probability of X
0	0.05
1	0.10
2	0.15
3	0.20
4	0.20
5	0.15
6	0.10
7	0.05

General instruction regarding the amount of capacity to build:

The general instruction regarding the amount of capacity to build is to minimize the total cost of capacity plus lost sales.

c)

Expert Solution

Summary Introduction

To determine: The principle that is illustrated in the problem.

Introduction:

Capacity planning is the process of planning the required production output based on the requirement or the demand that is predicted.

Explanation of Solution

Given information:

It is given that the cost of the lost sales is $20 per unit due to insufficient capacity. Assume that the cost is $7 for each unit of capacity built. In addition to this, the following information is given:

Demand - X units	Probability of X
0	0.05
1	0.10
2	0.15
3	0.20
4	0.20
5	0.15
6	0.10
7	0.05

Determine the principle that is illustrated in the problem:

In the given problem, the trade-off between excess capacity and lost sales is illustrated.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 5

Textbook Question

Answer 6

Textbook Question

Answer 7

a)

Expert Solution

Summary Introduction

To determine: The number of capacity units required to minimize the total cost of providing capacity plus lost sales.

Introduction:

Capacity planning is the process of planning the required production output based on the requirement or the demand that is predicted.

Explanation of Solution

Given information:

It is given that the cost of the lost sales is $20 per unit, due to insufficient capacity. Assume that the cost is $7 for each unit of capacity built. In addition to this, the following information is given:

Demand - X units	Probability of X
0	0.05
1	0.10
2	0.15
3	0.20
4	0.20
5	0.15
6	0.10
7	0.05

Build 0 units of capacity:

It is calculated by adding capacity cost and penalty cost.

Build 0 units of capacity=(7×0)+20[(0×0.05)+(1×0.10)+(2×0.15)+(3×0.20)+(4×0.20)+(5×0.15)+(6×0.10)+(7×0.05)]=0+20(0+0.10+0.30+0.60+0.80+0.75+0.60+0.35)=20×3.5=70

Build 1 unit of capacity:

It is calculated by adding capacity cost and penalty cost.

Build 1 unit of capacity=(7×1)+20[(0×(0.05+0.10))+(1×0.15)+(2×0.2)+(3×0.20)+(4×0.15)+(5×0.10)+(6×0.05)]=7+20(0+0.15+0.40+0.60+0.60+0.50+0.30)=7+(20×2.55)=58

Build 2 units of capacity:

It is calculated by adding capacity cost and penalty cost.

Build 2 units of capacity=(7×2)+20[(0×(0.05+0.10+0.15))+(1×0.20)+(2×0.2)+(3×0.15)+(4×0.10)+(5×0.05)]=14+20(0+0.20+0.40+0.45+0.40+0.25)=14+(20×1.7)=48

Build 3 units of capacity:

It is calculated by adding capacity cost and penalty cost.

Build 3 units of capacity=(7×3)+20[(0×(0.05+0.10+0.15+0.20))+(1×0.20)+(2×0.15)+(3×0.10)+(4×0.05)]=21+20(0+0.20+0.30+0.30+0.20)=21+(20×1)=41

Build 4 units of capacity:

It is calculated by adding capacity cost and penalty cost.

Build 4 units of capacity=(7×4)+20[(0×(0.05+0.10+0.15+0.20+0.20))+(1×0.15)+(2×0.10)+(3×0.05)]=28+20(0+0.15+0.20+0.15)=28+(20×0.50)=38

Build 5 units of capacity:

It is calculated by adding capacity cost and penalty cost.

Build 5 units of capacity=(7×5)+20[(0×(0.05+0.10+0.15+0.20+0.20+0.15))+(1×0.10)+(2×0.05)]=35+20(0+0.10+0.10)=35+(20×0.20)=39

Build 6 units of capacity:

It is calculated by adding capacity cost and penalty cost.

Build 6 units of capacity=(7×6)+20[(0×(0.05+0.10+0.15+0.20+0.20+0.15+0.10))+(1×0.05)]=42+20(0+0.05)=42+(20×0.05)=43

Build 7 units of capacity:

It is calculated by adding capacity cost and penalty cost.

Build 7 units of capacity=(7×7)+20[(0×(0.05+0.10+0.15+0.20+0.20+0.15+0.10+0.05))]=49+20(0)=49

Hence, the number of capacity units required (that has the minimum total cost of $38) to minimize the total cost of providing capacity plus lost sales is 4 units.

b)

Expert Solution

Summary Introduction

To determine: The general rule regarding the amount of capacity to build.

Introduction:

Capacity planning is the process of planning the required production output based on the requirement or the demand that is predicted.

Explanation of Solution

Given information:

It is given that the cost of the lost sales is $20 per unit due to insufficient capacity. Assume that the cost is $7 for each unit of capacity built. In addition to this, the following information is given:

Demand - X units	Probability of X
0	0.05
1	0.10
2	0.15
3	0.20
4	0.20
5	0.15
6	0.10
7	0.05

General instruction regarding the amount of capacity to build:

The general instruction regarding the amount of capacity to build is to minimize the total cost of capacity plus lost sales.

c)

Expert Solution

Summary Introduction

To determine: The principle that is illustrated in the problem.

Introduction:

Capacity planning is the process of planning the required production output based on the requirement or the demand that is predicted.

Explanation of Solution

Given information:

It is given that the cost of the lost sales is $20 per unit due to insufficient capacity. Assume that the cost is $7 for each unit of capacity built. In addition to this, the following information is given:

Demand - X units	Probability of X
0	0.05
1	0.10
2	0.15
3	0.20
4	0.20
5	0.15
6	0.10
7	0.05

Determine the principle that is illustrated in the problem:

In the given problem, the trade-off between excess capacity and lost sales is illustrated.

Answer 8

a)

Expert Solution

Summary Introduction

To determine: The number of capacity units required to minimize the total cost of providing capacity plus lost sales.

Introduction:

Capacity planning is the process of planning the required production output based on the requirement or the demand that is predicted.

Explanation of Solution

Given information:

It is given that the cost of the lost sales is $20 per unit, due to insufficient capacity. Assume that the cost is $7 for each unit of capacity built. In addition to this, the following information is given:

Demand - X units	Probability of X
0	0.05
1	0.10
2	0.15
3	0.20
4	0.20
5	0.15
6	0.10
7	0.05

Build 0 units of capacity:

It is calculated by adding capacity cost and penalty cost.

Build 0 units of capacity=(7×0)+20[(0×0.05)+(1×0.10)+(2×0.15)+(3×0.20)+(4×0.20)+(5×0.15)+(6×0.10)+(7×0.05)]=0+20(0+0.10+0.30+0.60+0.80+0.75+0.60+0.35)=20×3.5=70

Build 1 unit of capacity:

It is calculated by adding capacity cost and penalty cost.

Build 1 unit of capacity=(7×1)+20[(0×(0.05+0.10))+(1×0.15)+(2×0.2)+(3×0.20)+(4×0.15)+(5×0.10)+(6×0.05)]=7+20(0+0.15+0.40+0.60+0.60+0.50+0.30)=7+(20×2.55)=58

Build 2 units of capacity:

It is calculated by adding capacity cost and penalty cost.

Build 2 units of capacity=(7×2)+20[(0×(0.05+0.10+0.15))+(1×0.20)+(2×0.2)+(3×0.15)+(4×0.10)+(5×0.05)]=14+20(0+0.20+0.40+0.45+0.40+0.25)=14+(20×1.7)=48

Build 3 units of capacity:

It is calculated by adding capacity cost and penalty cost.

Build 3 units of capacity=(7×3)+20[(0×(0.05+0.10+0.15+0.20))+(1×0.20)+(2×0.15)+(3×0.10)+(4×0.05)]=21+20(0+0.20+0.30+0.30+0.20)=21+(20×1)=41

Build 4 units of capacity:

It is calculated by adding capacity cost and penalty cost.

Build 4 units of capacity=(7×4)+20[(0×(0.05+0.10+0.15+0.20+0.20))+(1×0.15)+(2×0.10)+(3×0.05)]=28+20(0+0.15+0.20+0.15)=28+(20×0.50)=38

Build 5 units of capacity:

It is calculated by adding capacity cost and penalty cost.

Build 5 units of capacity=(7×5)+20[(0×(0.05+0.10+0.15+0.20+0.20+0.15))+(1×0.10)+(2×0.05)]=35+20(0+0.10+0.10)=35+(20×0.20)=39

Build 6 units of capacity:

It is calculated by adding capacity cost and penalty cost.

Build 6 units of capacity=(7×6)+20[(0×(0.05+0.10+0.15+0.20+0.20+0.15+0.10))+(1×0.05)]=42+20(0+0.05)=42+(20×0.05)=43

Build 7 units of capacity:

It is calculated by adding capacity cost and penalty cost.

Build 7 units of capacity=(7×7)+20[(0×(0.05+0.10+0.15+0.20+0.20+0.15+0.10+0.05))]=49+20(0)=49

Hence, the number of capacity units required (that has the minimum total cost of $38) to minimize the total cost of providing capacity plus lost sales is 4 units.

Answer 9

a)

Expert Solution

Answer 10

a)

Expert Solution

Answer 11

Expert Solution

Answer 12

Summary Introduction

To determine: The number of capacity units required to minimize the total cost of providing capacity plus lost sales.

Introduction:

Capacity planning is the process of planning the required production output based on the requirement or the demand that is predicted.

Answer 13

Explanation of Solution

Given information:

It is given that the cost of the lost sales is $20 per unit, due to insufficient capacity. Assume that the cost is $7 for each unit of capacity built. In addition to this, the following information is given:

Demand - X units	Probability of X
0	0.05
1	0.10
2	0.15
3	0.20
4	0.20
5	0.15
6	0.10
7	0.05

Build 0 units of capacity:

It is calculated by adding capacity cost and penalty cost.

Build 0 units of capacity=(7×0)+20[(0×0.05)+(1×0.10)+(2×0.15)+(3×0.20)+(4×0.20)+(5×0.15)+(6×0.10)+(7×0.05)]=0+20(0+0.10+0.30+0.60+0.80+0.75+0.60+0.35)=20×3.5=70

Build 1 unit of capacity:

It is calculated by adding capacity cost and penalty cost.

Build 1 unit of capacity=(7×1)+20[(0×(0.05+0.10))+(1×0.15)+(2×0.2)+(3×0.20)+(4×0.15)+(5×0.10)+(6×0.05)]=7+20(0+0.15+0.40+0.60+0.60+0.50+0.30)=7+(20×2.55)=58

Build 2 units of capacity:

It is calculated by adding capacity cost and penalty cost.

Build 2 units of capacity=(7×2)+20[(0×(0.05+0.10+0.15))+(1×0.20)+(2×0.2)+(3×0.15)+(4×0.10)+(5×0.05)]=14+20(0+0.20+0.40+0.45+0.40+0.25)=14+(20×1.7)=48

Build 3 units of capacity:

It is calculated by adding capacity cost and penalty cost.

Build 3 units of capacity=(7×3)+20[(0×(0.05+0.10+0.15+0.20))+(1×0.20)+(2×0.15)+(3×0.10)+(4×0.05)]=21+20(0+0.20+0.30+0.30+0.20)=21+(20×1)=41

Build 4 units of capacity:

It is calculated by adding capacity cost and penalty cost.

Build 4 units of capacity=(7×4)+20[(0×(0.05+0.10+0.15+0.20+0.20))+(1×0.15)+(2×0.10)+(3×0.05)]=28+20(0+0.15+0.20+0.15)=28+(20×0.50)=38

Build 5 units of capacity:

It is calculated by adding capacity cost and penalty cost.

Build 5 units of capacity=(7×5)+20[(0×(0.05+0.10+0.15+0.20+0.20+0.15))+(1×0.10)+(2×0.05)]=35+20(0+0.10+0.10)=35+(20×0.20)=39

Build 6 units of capacity:

It is calculated by adding capacity cost and penalty cost.

Build 6 units of capacity=(7×6)+20[(0×(0.05+0.10+0.15+0.20+0.20+0.15+0.10))+(1×0.05)]=42+20(0+0.05)=42+(20×0.05)=43

Build 7 units of capacity:

It is calculated by adding capacity cost and penalty cost.

Build 7 units of capacity=(7×7)+20[(0×(0.05+0.10+0.15+0.20+0.20+0.15+0.10+0.05))]=49+20(0)=49

Hence, the number of capacity units required (that has the minimum total cost of $38) to minimize the total cost of providing capacity plus lost sales is 4 units.

Answer 14

b)

Expert Solution

Summary Introduction

To determine: The general rule regarding the amount of capacity to build.

Introduction:

Capacity planning is the process of planning the required production output based on the requirement or the demand that is predicted.

Explanation of Solution

Given information:

It is given that the cost of the lost sales is $20 per unit due to insufficient capacity. Assume that the cost is $7 for each unit of capacity built. In addition to this, the following information is given:

Demand - X units	Probability of X
0	0.05
1	0.10
2	0.15
3	0.20
4	0.20
5	0.15
6	0.10
7	0.05

General instruction regarding the amount of capacity to build:

The general instruction regarding the amount of capacity to build is to minimize the total cost of capacity plus lost sales.

Answer 15

b)

Expert Solution

Answer 16

b)

Expert Solution

Answer 17

Expert Solution

Answer 18

Summary Introduction

To determine: The general rule regarding the amount of capacity to build.

Introduction:

Capacity planning is the process of planning the required production output based on the requirement or the demand that is predicted.

Answer 19

Explanation of Solution

Given information:

It is given that the cost of the lost sales is $20 per unit due to insufficient capacity. Assume that the cost is $7 for each unit of capacity built. In addition to this, the following information is given:

Demand - X units	Probability of X
0	0.05
1	0.10
2	0.15
3	0.20
4	0.20
5	0.15
6	0.10
7	0.05

General instruction regarding the amount of capacity to build:

The general instruction regarding the amount of capacity to build is to minimize the total cost of capacity plus lost sales.

Answer 20

c)

Expert Solution

Summary Introduction

To determine: The principle that is illustrated in the problem.

Introduction:

Capacity planning is the process of planning the required production output based on the requirement or the demand that is predicted.

Explanation of Solution

Given information:

It is given that the cost of the lost sales is $20 per unit due to insufficient capacity. Assume that the cost is $7 for each unit of capacity built. In addition to this, the following information is given:

Demand - X units	Probability of X
0	0.05
1	0.10
2	0.15
3	0.20
4	0.20
5	0.15
6	0.10
7	0.05

Determine the principle that is illustrated in the problem:

In the given problem, the trade-off between excess capacity and lost sales is illustrated.

Answer 21

c)

Expert Solution

Answer 22

c)

Expert Solution

Answer 23

Expert Solution

Answer 24

Summary Introduction

To determine: The principle that is illustrated in the problem.

Introduction:

Capacity planning is the process of planning the required production output based on the requirement or the demand that is predicted.

Answer 25

Explanation of Solution

Given information:

It is given that the cost of the lost sales is $20 per unit due to insufficient capacity. Assume that the cost is $7 for each unit of capacity built. In addition to this, the following information is given:

Demand - X units	Probability of X
0	0.05
1	0.10
2	0.15
3	0.20
4	0.20
5	0.15
6	0.10
7	0.05

Determine the principle that is illustrated in the problem:

In the given problem, the trade-off between excess capacity and lost sales is illustrated.

Answer 26

Ch. 11 - Prob. 1DQ Ch. 11 - Prob. 2DQ Ch. 11 - A school district has forecast student enrollment...Ch. 11 - Prob. 4DQ Ch. 11 - Prob. 5DQ Ch. 11 - SOP or aggregate planning sometimes is confused...Ch. 11 - The XYZ Company manufactures a seasonal product....Ch. 11 - Prob. 8DQ Ch. 11 - Every firm has multiple objectives such as good...Ch. 11 - Prob. 10DQ

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