solutions chapter 5

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Lesson 07 Process Selection & Capacity Planning Solutions Solved Problem #1: see text book Solved Problem #2: see textbook Solved Problem #3: see textbook Solved Problem #4: see textbook (manual example) #1: 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 a variable cost of 70 cents per unit produced. Each item is sold to retailers at a price that averages 90 cents. Answer the following questions.

a. Display a graph of the cost, revenue relationship to volume.

Breakeven Analysis

Fixed Cost

Total Cost

Total Revenue

BEP is 460000

10,000

20,000

30,000

40,000

50,000

60,000

70,000

80,000

90,000

0 10,000 20,000 30,000 40,000 50,000 60,000 70,000 80,000 90,000 100,000

Volume

Dol

lars

b. What volume per month is required to break even? 46,000 units

c. What profit would be realized for a monthly volume of 61,000 units? 87,000 units?

$3,000 for 61,000 units; $8,200 for 87,000 units.

d. What volume is needed to obtain a profit of $16,000 per month? 126,000 units

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e. What volume is needed to obtain revenue of $23,000 per month? 25,555.5556 rounded to 25,556 units

#2: A small firm intends to increase the capacity of a bottleneck operation by adding a new machine. Two alternatives exist, machine A and machine B. The associated costs and revenues have been estimated as follows: annual fixed costs would be $40,000 for A and $30,000 for B; variable costs per unite would be $10 for A and $11 for B; and revenue per unit would be $15.

a. Determine the break even point for each alternative. Verify that there are two templates in this lesson which calculate this answer. A – 8,000 units; B – 7,500 units The Break even Analysis template can be used to calculate this answer; however, it requires you enter data for each alternative. The Multiple Alternative Analysis template also answers the same question as shown below.

Revenue/Unit 15

Cost Information -Alternative- Fixed Cost VC/Unit Trans Cost Break Even

A 40000 10 8000 B 30000 11 7500

b. Manually calculate the volume at the point of indifference between the two alternatives.

10,000 units

c. Use one of the lesson templates to verify the answer you obtained in b., and show a graph of the cost/volume relationship.

Costs Information

Pair Intersection Costs $ A B 10000 -140000

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Costs

AB

A B

-300,000.00

-250,000.00

-200,000.00

-150,000.00

-100,000.00

-50,000.00

0.000.00 5,000.00 10,000.00 15,000.00 20,000.00 25,000.00

Volume

Cos

ts

d. What is the total cost at the point of indifference?

$140,000

e. At what volume would the two alternatives yield the same profit? What is the profit at this volume? Show a graph of the profit/volume relationship. Profit is the same at a volume of 10,000 units. The profit at this volume is $10,000.

Revenue/Unit 15

Profit Information

Pair Intersection Profit

$ A B 10000 10000

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Profit

A

B

A B

-60,000.00

-40,000.00

-20,000.00

0.00

20,000.00

40,000.00

60,000.00

80,000.00

0.00 5,000.00 10,000.00 15,000.00 20,000.00 25,000.00

Volume

Prof

it

f. If the expected demand is 12,000 units, determine the costs and profits for each alternative? A: Costs - $160,000, Profit - $20,000 B: Costs - $162,000; Profit - $18,000

Volume Analysis

Volume 12000 Revenue/Unit 15 Total Costs Profit

-160000 20000 -162000 18000

#3: 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 are $25,000 per month are allocated to the operation which produces the pens, and variable costs are 37 cents per pen. Answer the following questions.

a. Find the monthly breakeven point if the pens sell for $1 each? 39,682.5397 rounded to 39,683 units

b. At what price (rounded to 2 decimal points) should the pens be sold to obtain a monthly profit of at least $15,000, assuming that monthly demand of 30,000 pens materializes? This is a manual problem! Price - $1.71

71.17033.1Re)000,30*37.000,25(000,30*Re000,15

)*(*RePr:int

toroundedvenuevenue

VolumeCostVariableCostsFixedVolumevenueofitH

L=+−=

+−=

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c. Verify the answer you obtained in b. by using the break even analysis template. What is the actual calculated profit using the price you obtained in b? Calculated profit - $15,200

Revenue/Unit 1.71 Variable Cost/Unit 0.37

Fixed Cost 25000

Breakeven Point 18656.7164

A volume of 30000 Reveune 51300

Variable Cost 11100 Total Cost 36100

Profit 15200

#4: 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. There are two possible alternatives for in-house production: Alternative A would have an annual fixed cost of $160,000 and a variable cost of $5 per unit; and alternative B would have an annual fixed cost of $190,000 and a variable cost of $4 per unit. Answer the following questions.

a. Display a graph of the cost/volume relationship.

Costs

Buy

A

B

-1,200,000.00

-1,000,000.00

-800,000.00

-600,000.00

-400,000.00

-200,000.00

0.000.00 20,000.00 40,000.00 60,000.00 80,000.00 100,000.00 120,000.00 140,000.00 160,000.00 180,000.00

Volume

Cos

ts

b. Over what volume range is Buy best? Buy is best when 0 <= Volume < 63,333.3333… units

c. Over what volume range is alternative A best?

A is never the best alternative

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d. Over what volume range is alternative B best? B is best when volume is > 63,333.333… units

e. What is the point of indifference between Buy and alternative B? What is the cost at this point?

Point of indifference – 63,333.333… units; cost - $443,333.33…

Costs Information Pair Intersection Costs $

Buy B 63333.3333 -443333.33

f. What is the point of indifference between the two in-house alternatives? What is the cost at this point?

Point of indifference between alternative A and B – 30,000 units; cost $310,000

Costs Information Pair Intersection Costs $

A B 30000 -310000 g. Assume the annual volume is 100,000 units, what is the cost for each alternative at this volume?

Buy – $700,000 A – $660,000 B – $590,000

Volume Analysis Volume 100000

Revenue/Unit Total Costs Profit

-700000 -660000 -590000

h. Assume the annual volume is 120,000 units and the products are sold for $10 each, what is the

profit for each alternative at this volume? Buy – $360,000 A – $440,000 B – $530,000

Volume Analysis Volume 120000

Revenue/Unit 10 Total Costs Profit

-840000 360000 -760000 440000 -670000 530000

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#5: A manager is trying to decide whether to purchase a certain part or to have it produced internally. Internal production could use either of two processes: IHA or IHB. IHA would entail a variable cost of $17 per unit and an annual fixed cost of $200,000. IHB would entail a variable cost of $14 per unit and an annual fixed cost of $240,000. Three vendors are willing to provide the part.

• Vendor A (VA) has a price of $20 per for any volume up to 30,000 units. • Vendor B (VB) has a price of $22 per unit for demand of 1,000 units or less, and $18 per unit for

larger quantities. • Vendor C offers a price of $21 per unit for the first 1,000 units and $19 for each additional unit

Answer the following questions. This is a manual problem.

a. If the manager anticipates an annual volume of 10,000 units what is the cost for each alternative?

IHA - $370,000 (200,000 + 17*10,000) IHB - $380,000 (240,000 + 14*10,000) VA - $200,000 (20*10,000) VB - $180,000 (18*10,000) VC - $192,000 (manually – 21*1,000 + 19*10,000)

b. Sketch the cost/volume relationship for Vendor each alternative on the same graph. c. Manually determine the point of indifference between the two internal alternatives.

13,333.3333… Hint: set the two equations equal to each other and solve for the volume IHA – 200,000 + 17*volume IHB – 240,000 + 14*volume

d. Can you use one of the templates in the lesson to determine the answer to c?

Yes.

Cost Information -Alternative- Fixed Cost VC/Unit Trans Cost

IHA 200000 17 IHB 240000 14

Costs Information

Pair Intersection Costs $

IHA IHB 13333.3333 -

426666.67

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Costs

IHA

IHB

IHA IHB

-700,000.00

-600,000.00

-500,000.00

-400,000.00

-300,000.00

-200,000.00

-100,000.00

0.000.00 5,000.00 10,000.00 15,000.00 20,000.00 25,000.00 30,000.00

Volume

Cos

ts

#6: A manager must decide which type of machine to buy A, B or C. Machine purchase costs are as follows Machine Purchase cost in $ A 40,000 B 30,000 C 80,000 Each machine can produce 4 products. The product forecasts and processing times on each machine is shown below: Processing Time (minutes/machine) Product Annual Demand (units) A B C 1 16,000 3 4 2 2 12,000 4 4 3 3 6,000 5 6 4 4 30,000 2 2 1 Answer the following questions. This is a manual problem.

a. How many processing minutes per year are needed for each machine?

A – 186,000 B – 208,000 C – 122,000

b. Assume machines operate 10 hours per day for 250 days per year, how many of each machine are

needed?

A – 2 machines (186,000/150,000 rounded up) B – 2 machines (208,000/150,000 rounded up) C – 1 machine (122,000/150,000 rounded up)

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c. Assume you are making your decision on which machine to buy on the lowest total purchase cost, which machine and how many would you buy? Buy 2 B’s because the total purchase cost is $60,000 (2*$30,000)

d. Consider the additional information: The machines differ in terms of hourly operating costs: A’s

have an hourly operating cost of $10, B’s have an hourly cost of $11; and, C’s have an hourly cost of $12. What is the total operating cost of each machine considering this additional information? Hints: Total operating cost = purchase cost + operating cost; and, convert processing minutes in a into processing hours)

A - $111,000 (80,000 + 31,000) B - $98,133 (60,000 + 38,133 rounded) C - $104,400 (80,000 + 24,400)

e. Based on total operating costs as defined in d, which machine and how many would you buy?

Buy 2 B’s because the total operating cost is lowest

#7: A manager must decide how many machines of a certain type to purchase. Each machine can process 100 customers per day. One machine will result in a fixed cost of $2,000 per day, while two machines will result in a fixed cost of $3,800 per day. Variable costs will be $20 per customer, and revenue will be $45 per customer. Answer the following questions.

a. Display a graph of the cost/revenue/volume relationship.

Breakeven Analysis

Total Cost 1 Machine

Total Cost 2 Machines

Total Revenue0.00

1,000.00

2,000.00

3,000.00

4,000.00

5,000.00

6,000.00

7,000.00

8,000.00

9,000.00

10,000.00

0 50 100 150 200 250

Volume

Dol

lars

b. Calculate the daily break even volume for 1 machine and 2 machines?

1 machine – 80 customers 2 machines – 152 customers

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Revenue/Unit 45 -Step Fixed Costs- Variable Cost/Unit 20 1 Machine 2 Machines

Fixed Cost 2000 3800 Range of Volume 100 200 Breakeven Point 80 152

c. What is the profit at the break even volume? Hint: you do not need a template to answer this,

merely recall the definition of the break even volume. By definition the profit at the break even volume is 0 because it is the volume where total revenue = total costs.

d. If the range of customer volume is between 90 and 120 customers per day; how many machines should the manager buy? Why?

The manager should buy 1 machine. Between 90 and 100 customers, the manager can make a profit; however with 2 machines the manager will never make a profit because the break even volume is 152 units.

e. What is the profit the manager will make if the customer demand is 90?

$250

Low Demand Analysis 1 Machine 2 Machines

Volume 90 90 Revenue 4050 4050

Variable Cost 1800 1800 Total Cost 3800 5600

Profit 250 -1550 Profitable Profitable Un-profitable

f. What is the profit the manager will make if the customer demand is 100? Hint: You can use the lesson template to answer this question without doing it manually.

$500

Low Demand Analysis 1 Machine 2 Machines

Volume 100 100 Revenue 4500 4500


Profit 500 -1300 Profitable Profitable Un-profitable

g. How much will the manager lose if he/she buys 2 machines and the customer demand is 101?

$1,275

High Demand Analysis

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1 Machine 2 Machines Volume 100 101

Revenue 4500 4545 Variable Cost 2000 2020

Total Cost 4000 5820 Profit 500 -1275

Profitable Profitable Un-profitable

h. What should the manager do if he/she only buys one machine and more than 100 customers show up on a given day? What would you do?

The manager has several options: one, turn the customer away and apologize for not being able to serve them; two, give them a rain check for another day with a discount; …..

#8: 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 per month, and two lines will mean a fixed cost of $10,500 per month. Each line will be able to process 15 cars per hour. Variable costs will be $3 per car and revenue will be $5.95 per car. The car wash operates 300 hours per month.

a. Display a graph of the monthly cost/revenue/volume relationship.

Breakeven Analysis

Total Cost 1 Line

Total Cost 2 Lines

Total Revenue0.00

10,000.00

20,000.00

30,000.00

40,000.00

50,000.00

60,000.00

0 1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000 10,000

Volume

Dol

lars

b. Calculate the monthly break even volume for 1 line and 2 lines?

1 line – 2,033.89831 rounded to 2034 cars 2 lines –3,559.32203 rounded to 3560 cars

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Revenue/Unit 5.95 -Step Fixed Costs- Variable Cost/Unit 3 1 Line 2 Lines

Fixed Cost 6000 10500 Range of Volume 4500 9000 Breakeven Point 2033.89831 3559.32203

c. If the range of customer volume is between 14 and 18 cars per hour; how many lines should the manager install? Why?

The manager should have 1 line. Between 14 and 18 cars per hour equates to between 4,200 and 5,400 cars per month. The manager will make more profit with 1 line than with 2 lines.

Just in case you are not able to answer this question, d – g provide some insight to the answer. Do them and then see if you can answer c. d. What is the monthly profit the manager will make if the demand is 4200 cars and he/she installs

one line?

$6,390

Low Demand Analysis 1 Line 2 Line

Volume 4200 4200 Revenue 24990 24990


Profit 6390 1890 Profitable Profitable Profitable

e. What is the monthly profit the manager will make if the demand is 4200 cars and he/she installs two lines?

$1,890 (see the previous answer template result)

f. What is the maximum monthly profit the manager can make for the demand range scenario if

he/she installs one line?

Under the demand scenario, one line can handle a maximum of 4500 cars per month. The maximum profit is realized with this volume and is $7,275.

Low Demand Analysis 1 Line 2 Lines

Volume 4500 4500 Revenue 26775 26775



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g. What is the maximum monthly profit the manager can make for the demand range scenario if he/she installs two lines?

The demand scenario upper limit is 5,400 cars per month. The maximum profit is realized with this volume and is $5,430.

High Demand Analysis 1 Line 2 Lines

Volume 4500 5400 Reveune 26775 32130



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