Chapter 5 Homework
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University of Wisconsin, Stout *
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200
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Industrial Engineering
Date
Dec 6, 2023
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xlsx
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14
Uploaded by nadiareese1
Utilization = Actual output / Design capacity
Utilization = 4 / 6*100
66.67
80
Determine the utilization and efficiency for each of the following situations.
a. A loan processing operation that processes an average of 7 loans per day. The operation has a design capacity of 10 loans per day and an effective capacity of 8 loans per day.
70 = 7 / 10*100
Efficiency = Actual output / Effective capacity
87.5 = 7 / 8*100
b. A furnace repair team that services an average of four furnaces a day if the design capacity is six furnaces a day and the effective capacity is five furnaces a day.
Efficiency = 4 / 5*100
c. Would you say that systems that have higher efficiency ratios than other systems will always have higher utilization ratios than those other systems? Explain.
When compared to other systems, a loan processing team that has greater efficiency ratios will always have higher utilization ratios.
61,000 x 0.2 = 12,000
87,000 x 0.2 = 17,400
16,000 = (0.2 x Q) - 9,200
126,000
25,555.5556 rounded to 25,556 units
A producer of pottery is considering the addition of a new plant to absorb the backlog of demand that now exists. The primary location being considered will have fixed costs of $9,200 per month and vari-able costs of 70 cents per unit produced. Each item is sold to retailers at a price that averages 90 cents.
a. What volume per month is required in order to break even?
9,200 / (.90 - .70) = 46,000
b. What profit would be realized on a monthly volume of 61,000 units? 87,000 units?
12,000 - 9,200 = $3,000
17,400 - 9,200 = $8,200
c. What volume is needed to obtain a profit of $16,000 per month?
d. What volume is needed to provide a revenue of $23,000 per month?
Total Cost
Total Revenue
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a. Find the break-even quantity if pens sell for $1 each.
Break-even point units = Fixed Costs / (selling price - variable costs)
Profit = Revenue - costs
$15,000 = (x)(30,000) - $25,000 - .37(30,000)
$15,000 = 30,000x - 36,100
$51,100 = 30,000x
x = $1.73
A producer of felt-tip pens has received a forecast of demand of 30,000 pens for the coming month from its marketing department. Fixed costs of $25,000 per month are allocated to the felt-tip opera-tion, and variable costs are 37 cents per pen.
25,000 / (1 - 0.37) = 39,682.53968 = 39,683 (rounded off)
b. At what price must pens be sold to obtain a monthly profit of $15,000, assuming that estimated demand materializes?
Option One: BEP = (160,000 / (7 - 5)) = 80,000
Option Two: BEP = (190,000 / (7 - 4)) = 63,333
A firm plans to begin production of a new small appliance. The manager must decide whether to purchase the motors for the appliance from a vendor at $7 each or to produce them in-house. Either of two pro-cesses could be used for in-house production; one would have an annual fixed cost of $160,000 and a variable cost of $5 per unit, and the other would have an annual fixed cost of $190,000 and a variable cost of $4 per unit. Determine the range of annual volume for which each of the alternatives would be best.
If the yearly output is estimated to be fewer than 63,333 units, purchasing from the vendor is the best alternative. Option Two is the best choice if yearly output is estimated to be between 63,333 and 80,000 units. Option One is the best choice if the estimated yearly output is larger than 80,000 units.
Two years annual demand = annual demand × triple
50,000 x 3 = 150,000 units
225 x 240 = 54,000
A company manufactures a product using two machine cells. Each cell has a design capacity of 250 units per day and an effective capacity of 230 units per day. At present, actual output aver-ages 200 units per cell, but the manager estimates that productivity improvements soon will increase output to 225 units per day. Annual demand is currently 50,000 units. It is forecasted that, within two years, annual demand will triple. How many cells should the company plan to produce to satisfy predicted demand under these conditions? Assume 240 workdays per year.
Output = increase output × number of workdays per year
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150,000 / 54,000 = 2.78 (rounded)
a.
Total time = Total demand for each product * Processing time
A
Machine A
B
C
Machine cost = 1 $40,000 = $40,000
∗
Machine B
Machine cost = 1 $30,000 = $30,000
∗
Machine C
Machine cost = 1 $80,000 = $80,000
∗
(16,000 3) + (12,000 4) + (6,000 5) + (30,000 2) = $186,000
∗
∗
∗
∗
Number of machine = 186,000 / (250 10 60)
∗
∗
Number of machine = 1 (Round off)
(16,000 4) + (12,000 4) + (6,000 6) + (30,000 2) = $208,000
∗
∗
∗
∗
Number of machine = 208,000 / (250 10 60)
∗
∗
Number of machine = 1 (Round off)
(16,000 2) + (12,000 3) + (6,000 4) + (30,000 1) = $122,000
∗
∗
∗
∗
Number of machine = 122,000 / (250 10 60)
∗
∗
Number of machine = 1 (Round off)
b.
186,000 / 60 = 3,100 hrs × $10 = $31,000 + $80,000 = $111,000
208,000 / 60 = 3,466.67 hrs × $11 = $38,133 + $60,000 = $98,133
122,000 / 60 = 2,033.33 hrs × $12 = $24,400 + $80,000 = $104,400
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15 cars/hour * 300 hours/month = 4,500 cars per month
4,500 cars * $5.95 per car = $26,775
2 * $26,775 = $53,550
For one wash line:
Fixed cost: $6,000
Variable cost: 4,500 cars * $3 per car = $13,500
Total cost: $6,000 + $13,500 = $19,500
For two wash lines:
Fixed cost: $10,500
Variable cost: 2 * 4,500 cars * $3 per car = $27,000
Total cost: $10,500 + $27,000 = $37,500
The manager of a car wash must decide whether to have one or two wash lines. One line will mean a fixed cost of $6,000 a month, and two lines will mean a fixed cost of $10,500 a month. Each line would be able to process 15 cars an hour. Variable costs will be $3 per car, and revenue will be $5.95 per car. The manager projects an average demand of between 14 and 18 cars an hour. Would you recommend one or two lines? The car wash is open 300 hours a month.
Based on this analysis, I would recommend the manager to choose the option of having two wash lines. This would lead to a higher revenue and a profitable operation for the car wash.
Given the following diagram,
a. What is the capacity of this system?
I would say either 15 or 17…
The maximum capacity of the given system is 15 units/hour because circles 2 and 5 only can perform 15 units per hour
b. If the capacity of one operation could be increased in order to increase the output of the system, which operation should it be, and what amount of increase?
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a. What is the current capacity of the entire system?
Not sure how to solve
Not sure how to solve
The following diagram describes a service process where customers go through through either of two parallel three-step processes and then merge into a single line for two final steps.
b. If you could increase the capacity of only one operation through process improvement efforts, which operation would you select, how much additional capacity would you strive for, and what would the resulting capacity of the process be?
Payback time = Initial cost / Annual savings
A new machine will cost $18,000, but it will result in a savings of $2,400 per year. What will the payback time be in years?
Payback time = $18,000 / $2,400 = 7.5 years