The Craine Company manufactures three products, which require three resources – labour, materials, and administration. The unit profits on these products are $10, $6, and $4 respectively. There are 100 hr of labour, 600 lb of material, and 300 hr of administrations available per day. In order to determine the optimal product mix, the following LP model is formulated and solved:   Maximize Z =10 x 1 +6 x 2 +4 x 3 Subject to          x1+x2+x3 ≤100 labour                                   10x1+4x2+5x3 ≤600 material 2x1+2x2+6x3 ≤300 administration        x1+x2+x3 ≥0 Where x1,x2, and x3are the daily production levels of products 1, 2, and 3 respectively. A computer output of the solution given below:   Optimal Solution: x1 = 33.33, x2 = 66.67, x3 = 0 Optimal Value: Maximum profit = $733.33 Shadow Prices: For row 1 = $3.33, for row 2 = 0.67, for row 3 = 0 Opportunity Costs For x1 = 0, for x2 = 0, for x3 = 2.67   Ranges on Objective Function Coefficients Row Lower Limit Present Value Upper Limit x1 6 10 15 x2 4 6 10 x3 -∞ 4 6.67     Ranges on Right-Hand-Side (RHS) Constraints Row Lower Limit Present Value Upper Limit 1 60 100 150 2 400 600 1000 3 200 300 ∞   Explain the sensitivity analysis from the problem above.

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Chapter1: Making Economics Decisions
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The Craine Company manufactures three products, which require three resources – labour, materials, and administration. The unit profits on these products are $10, $6, and $4 respectively. There are 100 hr of labour, 600 lb of material, and 300 hr of administrations available per day. In order to determine the optimal product mix, the following LP model is formulated and solved:

 

Maximize Z =10 +6 +4 3

Subject to          x1+x2+x3 ≤100 labour

                                  10x1+4x2+5x3 ≤600 material

2x1+2x2+6x3 ≤300 administration

       x1+x2+x3 ≥0

Where x1,x2, and x3are the daily production levels of products 1, 2, and 3 respectively.

A computer output of the solution given below:

 

Optimal Solution:

x1 = 33.33, x= 66.67, x3 = 0

Optimal Value:

Maximum profit = $733.33

Shadow Prices:

For row 1 = $3.33, for row 2 = 0.67, for row 3 = 0

Opportunity Costs

For x1 = 0, for x2 = 0, for x3 = 2.67

 

Ranges on Objective Function Coefficients

Row

Lower Limit

Present Value

Upper Limit

x1

6

10

15

x2

4

6

10

x3

-∞

4

6.67

 

 

Ranges on Right-Hand-Side (RHS) Constraints

Row

Lower Limit

Present Value

Upper Limit

1

60

100

150

2

400

600

1000

3

200

300

 

Explain the sensitivity analysis from the problem above.

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