98. A linear programming problem has the following objective function: 20X + 40Y + 60Z.
If the optimal solution provided by the model is to produce and sell 100, 200, and 300 units of X, Y, and Z,
respectively, what is the expected return?
99. Hasselblad Company manufactures two different products, X and Y. The company has 100 pounds of
materials and 300 direct labor hours available for production.
The time requirements and contribution margins per unit are as follows:
Product X
Product Y
Contribution margin per unit
$5
$6
Materials per unit (lbs.)
2
3
Direct labor hours per unit
5
3
What is the objective function for maximizing profits?
100. Hasselblad Company manufactures two different products, X and Y. The company has 100 pounds of
materials and 300 direct labor hours available for production.
The time requirements and contribution margins per unit are as follows:
Product X
Product Y
Contribution margin per unit
$5
$6
Materials per unit (lbs.)
2
3
Direct labor hours per unit
5
3
What is the equation for the constraint on materials?
101. Hasselblad Company manufactures two different products, X and Y. The company has 100 pounds of
materials and 300 direct labor hours available for production.
The time requirements and contribution margins per unit are as follows:
Product X
Product Y
Contribution margin per unit
$5
$6
Materials per unit (lbs.)
2
3
Direct labor hours per unit
5
3
What is the equation for the constraint on direct labor?
102. Figure 20-4
Montgomery Company produces A and B with contribution margins per unit of $40 and $30, respectively. Only
500 labor hours and 300 machine hours are available for production.
Time requirements to produce one unit of A and B are as follows:
Product A
Product B
Labor hours per unit
6
3
Machine hours per unit
2
5
Refer to Figure 20-4. What is the objective function to maximize profits for Montgomery Company?
103. Figure 20-4
Montgomery Company produces A and B with contribution margins per unit of $40 and $30, respectively. Only
500 labor hours and 300 machine hours are available for production.
Time requirements to produce one unit of A and B are as follows:
Product A
Product B
Labor hours per unit
6
3
Machine hours per unit
2
5
Refer to Figure 20-4. What is the constraint on labor hours for Montgomery Company?
104. Figure 20-4
Montgomery Company produces A and B with contribution margins per unit of $40 and $30, respectively. Only
500 labor hours and 300 machine hours are available for production.
Time requirements to produce one unit of A and B are as follows:
Product A
Product B
Labor hours per unit
6
3
Machine hours per unit
2
5
Refer to Figure 20-4. What is the constraint on machine hours for Montgomery Company?
105. Knoxville Manufacturing Company produces X and Y with contribution margins per unit of $10 and $90,
respectively. Only 200 labor hours and 400 machine hours are available for production.
Time requirements to produce one unit of X and Y are as follows:
Product X
Product Y
Labor hours per unit
1
2
Machine hours per unit
5
1
What is the constraint on machine hours for Knoxville Manufacturing Company?
106. Knoxville Manufacturing Company produces X and Y with contribution margins per unit of $10 and $90,
respectively. Only 200 labor hours and 400 machine hours are available for production.
Time requirements to produce one unit of X and Y are as follows:
Product X
Product Y
Labor hours per unit
1
2
Machine hours per unit
5
1
What is the constraint on labor hours for Knoxville Manufacturing Company?
107. Knoxville Manufacturing Company produces X and Y with contribution margins per unit of $10 and $90,
respectively. Only 200 labor hours and 400 machine hours are available for production.
Time requirements to produce one unit of X and Y are as follows:
Product X
Product Y
Labor hours per unit
1
2
Machine hours per unit
5
1
What is the objective function to maximize profits for Knoxville Manufacturing Company?
108. The following information is available for Woodside Furniture Company, which sells two products:
Chair X
Chair Y
Processing time
4 hours
6 hours
Metal used
30 sq. ft.
18 sq. ft.
Selling price
$200.00
$100.00
Variable cost
$150.00
$60.00
Fixed cost
$30.00
$30.00
There are 200 hours available in the plant and 200 square feet of metal available per operating period.
The constraint equation representing processing time available is
109. The following information is available for Woodside Furniture Company, which sells two products:
Chair X
Chair Y
Processing time
4 hours
6 hours
Metal used
30 sq. ft.
18 sq. ft.
Selling price
$200.00
$100.00
Variable cost
$150.00
$60.00
Fixed cost
$30.00
$30.00
There are 200 hours available in the plant and 200 square feet of metal available per operating period.
What is the objective function for maximizing sales?
110. Figure 20 – 5
The Golden Wheels Trailer Company recorded the following information for two of their trailers:
Trailer A
Trailer B
Processing time
3 hours
5 hours
Vinyl cover used
17 sq. ft.
13 sq. ft.
Selling price
$60.00
$90.00
Variable cost
$45.00
$60.00
Fixed cost
$20.00
$30.00
There are 100 hours available in the plant and 75 square feet of vinyl available per operating period.
Refer to Figure 20-5. What is the objective function for maximizing profits?
111. Figure 20 – 5
The Golden Wheels Trailer Company recorded the following information for two of their trailers:
Trailer A
Trailer B
Processing time
3 hours
5 hours
Vinyl cover used
17 sq. ft.
13 sq. ft.
Selling price
$60.00
$90.00
Variable cost
$45.00
$60.00
Fixed cost
$20.00
$30.00
There are 100 hours available in the plant and 75 square feet of vinyl available per operating period.
Refer to Figure 20-5. The constraint equation representing the materials available for the production processes is
112. Figure 20 – 5
The Golden Wheels Trailer Company recorded the following information for two of their trailers:
Trailer A
Trailer B
Processing time
3 hours
5 hours
Vinyl cover used
17 sq. ft.
13 sq. ft.
Selling price
$60.00
$90.00
Variable cost
$45.00
$60.00
Fixed cost
$20.00
$30.00
There are 100 hours available in the plant and 75 square feet of vinyl available per operating period.
Refer to Figure 20-5. Which of the following statements is INCORRECT?
113. Using the graphic approach to linear programming, the solution is usually
114. In the graphic method of solving a linear programming problem, which of the following is depicted on the
graph?
115. Theory of constraints focuses on what three operation measures of system performance?
116. The theory of constraints focuses on each of the following measures of organizational performance
EXCEPT
117. Which of the following is TRUE about the theory of constraints?
118. Which of the following is NOT a step in the methodology for improving performance under the theory of
constraints?
119. The theory of constraints uses the following five steps to achieve its goal of improving organizational
performance:
1.
Exploit the binding constraints.
2.
Elevate the organization’s binding constraints.
3.
Identify an organization’s constraints.
4.
Repeat the process as a new constraint emerges to limit output.
5.
Subordinate everything else to the decisions made when exploiting the binding constraints.
What is the correct order for performing these steps?
120. A drummer is(are)
121. The shadow price
122. The drum-buffer-rope system is another name for
123. Following is information pertaining to material that is used in the assembly of motorcycles:
Annual demand
5,000 units
Unit cost
$30
Cost of placing an order
$700
Carrying cost as a percentage of unit cost
12%
Required:
a.
Calculate total annual carrying costs for an order quantity of 200 units per order.
b.
Calculate total annual ordering costs for an order quantity of 200 units per order.
c.
Determine the optimal order size.
($30 ´ 0.12) ´ (200/2) = $360
b.
$700 ´ (5,000/200) = $17,500
EOQ = = 1,394.43 units
124. Harrisburg Company uses quantitative models for inventory control. For canned syrup, the annual demand
is 9,000 cases. The supplier is 500 miles away, and it usually takes 4 days to get an order filled. The average
order costs $18 to process and the carrying cost per case is $42 per year. The store is open 300 days a year.
Required:
a.
Determine the economic order quantity.
b.
Determine the reorder point if a safety stock of 24 cases is desired.
Economic order quantity = = 88 cases
b.
Reorder point = [(9,000/300) ´ 4] + 24 = = 144 cases
125. Sweet Tooth Company manufactures candy. The company buys chocolate used in the candy in 10-pound
boxes that cost $10 each. The company uses 30,000 of the boxes per year, and usage occurs evenly throughout
the year.
The average cost to carry a 10-pound box in inventory per year is $4, and the cost to place an order is $3.
Required:
a.
Determine the economic order quantity for the chocolate in terms of 10-pound boxes.
b.
If the company works 250 days per year, on the average, how many boxes of chocolate are used per working day?
c.
If the lead time for an order is normally eight working days, determine the reorder point for chocolate.
d.
If 50 boxes of chocolate are carried as safety stock, determine the reorder point for the chocolate.
126. Harrowing Company has the following information:
Annual demand
3,500 units
Order size
500 units
Ordering cost per order
$400
Carrying costs per unit for one year
$40
Lead time (maximum 20 days)
10 days
Maximum daily use
25 units
Work year
250 days
Required:
a.
Determine the economic order quantity for Harrowing.
b.
What is the annual savings to Harrowing Company if it was to change from an order size of 1,000 to the economic order quantity?
c.
What is the reorder point?
d.
What is the safety stock needed to prevent stockouts?
EOQ = = 264.58 units
b.
Total costs (500 units) =
[$400 ´ (3,500/500)] + [$40 ´ (500/2)] =
$12,800
Total costs (264.58 units) =
[$400 ´ (3,500/264.58)] + ($40 ´ (264.58/2)] =
10,583
Annual savings
$2,217
EOQ =
b.
120 boxes
30,000/250
c.
960 boxes
(120 x 8)
d.
1,010 boxes
(120 x 8) + 50
127. Answer the following questions pertaining to just-in-time inventory management:
a.
What are key elements of the JIT philosophy?
b.
What elements of the JIT approach contribute to reducing materials inventory?
c.
Why do proponents of JIT believe inventory is an enemy?
Maximum lead time
´ 20
Maximum lead time demand
500 units
Reorder point without safety stock
140 units
128. The following reasons have been offered for holding inventories:
1.
To balance ordering or setup costs and carrying costs.
2.
To satisfy customer demand (e.g., meet delivery dates).
3.
To avoid shutting down manufacturing facilities because of
(a) machine failure.
(b) defective parts.
(c) unavailable parts.
4.
Unreliable production processes.
5.
To take advantage of discounts.
6.
To hedge against future price increases.
Required:
a.
Explain how the JIT approach responds to each of these reasons and, consequently, argues for insignificant levels of inventories.
b.
The theory of constraints (TOC) criticizes the JIT approach to inventory management, arguing that it fails to protect throughput. Explain
what this means and describe how TOC addresses this issue.
levels.
manufacturing.
6.
JIT emphasizes long-term contracts that stipulate prices and acceptable quality levels.
129. Lexamoor Products Corporation produces two products. The manufacture of these products is partially
automated. Total available labor hours are 400, and the total available machine hours are 600. Time
requirements and contribution margins per unit for each product are as follows:
Product X
Product Y
Labor hours
2
3
Machine hours
4
2
Contribution margin per unit
$5
$4
Required:
a.
What is the equation to be maximized?
b.
What are the equations that express the constraints?
c.
What is the greatest number of units of X that can be produced given the constraints?
d.
What is the optimal solution?
130. Commonwealth Dry Cleaners has 400 hours a week available to use in dry cleaning or laundry. Four
thousand inches of hanging space is available. The average item that is dry cleaned takes six inches of hanging
space, whereas laundry items take up only three inches of hanging space. The contribution margin for laundry
items averages $3.50; dry cleaned items average $6.50. Fifty items can be washed per hour, whereas only
twenty can be dry cleaned.
Required:
a.
Determine the objective function. Is it a minimization or maximization function?
b.
Set up the constraint equations.
a.
Objective function:
Maximize $3.50(L) + $6.50(D)
b.
Hours available:
0.02(L) + 0.05(D) £ 400
Hanging space:
3.00(L) + 6.00(D) £ 4,000
a.
Maximize $5X + $4Y
b.
Labor hours:
2X + 3Y £ 400
Machine hours:
4X + 2Y £ 600
400/2 = 200
600/4 = 150
d.
X = 125 units, Y = 50 units.
131. Woodcrafters Corporation manufactures two different miniature models of furniture, a table and a chair.
The company has 500 feet of lumber, 400 machine hours, and 600 direct labor hours available for production.
The miniature tables and chairs provide $5 and $4 of contribution margin, respectively.
The time and lumber requirements to build a miniature table or chair are as follows:
Table
Chair
Feet of lumber per unit
5
2
Machine hours per unit
2
3
Direct labor hours per unit
4
2
Required:
a.
What is the objective function being maximized?
b.
What are the constraint equations?
c.
Graph the constraint equations. Identify the feasible region.
d.
What is the optimal solution?
Maximize
$5T + $4C
b.
Lumber:
5T + 2C £ 500
Machine hours:
2T + 3C £ 400
Labor hours:
4T + 2C £ 600
d.
There are three possible corner solutions:
(1)
T = 100, C = 0
CM = $5(100) + $4(0) = $500
(2)
T = 0, C = 133.333
CM = $5(0) + $4(133.333) = $533.33
(3)
T = 63.64, C = 90.91
CM = $5(63.64) + $4(90.91) = $681.84
132. Iron Horses Corporation produces two types of motorcycle frames, (Frame X and Frame Y). Frame X
passes through four processes: Cutting, Welding, Polishing, and Painting. Frame Y uses three of the same
processes: Cutting, Welding, and Painting. Each of the four processes employs forty workers who work eight
hours each day. Frame X sells for $80 per unit, and Frame Y sells for $110 per unit. Materials is the only unit-
level variable expense. The materials cost for Frame X is $40 per unit, and the materials cost for Frame Y is $50
per unit. Iron Horses’ accounting system has provided the following additional information about its operations
and products:
Resource
Resource
Usage/Unit
Usage/Unit
Resource Name
Resource Available
Frame X
Frame Y
Cutting labor
19,200 minutes
30 minutes
20 minutes
Welding labor
19,200 minutes
30 minutes
60 minutes
Polishing labor
19,200 minutes
30 minutes
–
Painting labor
19,200 minutes
20 minutes
30 minutes
Market demand: X
400 per day
1 unit
–
Market demand: Y
200 per day
–
1 unit
Iron Horses’ management has determined that any production interruptions can be corrected within two days.
Required:
a.
Assuming that Iron Horses can meet daily market demand, compute the potential daily profit. Now compute the minutes needed for each
process to meet the daily market demand. Can Iron Horses meet daily market demand? If not, where is the bottleneck? Can you derive an
optimal mix without using a graphical solution? If so, explain how.
b.
Explain how a drum-buffer-rope system would work for Iron Horses.
Potential daily sales:
Frame X
Frame Y
Sales
$ 110
Materials
CM per unit
$ 60
Daily demand
400
200
Daily profit
$16,000
$12,000
Process
Resource Demands
Resource Supply
Cutting
12,000
4,000
16,000
19,200
Welding
12,000
12,000
24,000
19,200
Polishing
12,000
19,200
Painting
8,000
6,000
14,000
19,200
133. Grapevine Incorporated produces two different barrels used in winemaking. (X and Y) The company has
three processes, cutting, forming, and curing. In cutting, the wood is cut to size and prepared for forming. In
forming, the wood is bent to shape and connected together to form the barrel. In curing, the seams are finished
and the oak is left to process. In cutting, setup time is 1/2 hour. The other two processes do not have any setup
time. The demand for Component X is 90 units per day and the demand for Component Y is 240 units per day.
The minutes required per unit for each component are as follows:
Cutting
Forming
Curing
Component X
30
12
8
Component Y
20
15
6
The company operates one 8-hour shift. The cutting process employs 10 workers. Two hours of their time is used for setup. The forming process is
the most labor intensive and has 15 workers. The curing department is not labor intensive—the only significant unit-level variable costs are materials
and power. The department only employs 6 associates. For component X, the variable cost is $40 per unit and for Component Y, it is $30 per unit.
The selling price per barrel is $95 for Component X and $80 for Component Y.
Required:
a.
Calculate the estimated daily potential profit.
b.
Calculate the resources available in minutes for each area.
c.
Calculate the resources demanded in minutes for each area and identify any bottlenecks.
d.
What is the contribution margin per unit of bottleneck resource and what does that imply?
X.
potential