Chapter 25 – The application of linear programming to management accounting
MULTIPLE CHOICE
1. A linear programming problem has an objective function of 10X + 12Y. If the optimal solution
provided by the model is to produce and sell 400 units of X and 1,000 units of Y, the expected return is
a.
£1,400.
b.
£40,800.
c.
£14,800.
d.
£16,000.
2. A linear programming model would NOT include which of the following items?
a.
independent variables
b.
networks
c.
dependent variables
d.
objective function
Figure 25-1
Hassel Company manufactures two different products, X and Y. The company has 100 kgs of
materials and 300 direct labour hours available for production.
The time requirements and contribution margins per unit are as follows:
Product X
Product Y
Contribution margin per unit
£4
£5
Materials per unit (lbs.)
1
2
Direct labour hours per unit
4
2
3. Refer to Figure 25-1. What is the objective function for maximizing profits?
a.
Minimize £4X + £5Y
b.
Maximize £4X + £5Y
c.
Maximize £1X + £2Y
d.
Maximize £4X + £2Y
4. Refer to Figure 25-1. What is the equation for the constraint on materials?
a.
£1X + £2Y 100
b.
£4X + £2Y 100
c.
£4X + £5Y 100
d.
£4X + £5Y 300
5. Refer to Figure 25-1. What is the equation for the constraint on direct labour?
a.
£1X + £2Y 300
b.
£4X + £2Y 100
c.
£4X + £5Y 100
d.
£4X + £2Y 300
6. 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?
a.
£36,000
b.
£28,000
c.
£120
d.
£24,000
Figure 25-2
Heft Company produces A and B with contribution margins per unit of £40 and £30, respectively.
Only 500 labour 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
Labour hours per unit
5
2
Machine hours per unit
1
4
7. Refer to Figure 25-2. What is the objective function to maximize profits for Heft Company?
a.
Minimize 5A + 2B
b.
Maximize 1A + 4B
c.
Maximize 40A + 30B
d.
Minimize 40A + 30B
8. Refer to Figure 25-2. What is the constraint on labour hours for Heft Company?
a.
5A + 1B 500
b.
5A + 2B 500
c.
1A + 4B 300
d.
40A + 30B 500
9. Refer to Figure 25-2. What is the constraint on machine hours for Heft Company?
a.
1A + 4B 500
b.
5A + 2B 500
c.
1A + 4B 300
d.
40A + 30B 500
Figure 25-3
Tiffany Manufacturing Company produces X and Y with contribution margins per unit of £10 and
£90, respectively. Only 200 labour hours and 400 machine hours are available for production.
Time requirements to produce one unit of X and Y are as follows:
Product A
Product B
Labour hours per unit
1
2
Machine hours per unit
5
1
10. Refer to Figure 25-3. What is the constraint on machine hours for Tiffany Manufacturing Company?
a.
10X + 90Y 200
b.
1X + 2Y 400
c.
1X + 2Y 200
d.
5X + 1Y 400
11. Refer to Figure 25-3. What is the constraint on labour hours for Tiffany Manufacturing Company?
a.
10X + 90Y 200
b.
1X + 2Y 400
c.
1X + 2Y 200
d.
1X + 4Y 400
12. Refer to Figure 25-3. What is the objective function to maximize profits for Tiffany Manufacturing
Company?
a.
Minimize 10X + 90Y
b.
Maximize 1X + 2Y
c.
Maximize 10X + 90Y
d.
Minimize 1X + 2Y
Figure 25-4
The following information is available for Wilson Trailer Company, which sells two products:
Trailer A
Trailer B
Processing time
2 hours
4 hours
Vinyl cover used
16 sq. ft.
12 sq. ft.
Selling price
£50.00
£80.00
Variable cost
£35.00
£50.00
Fixed cost
£10.00
£20.00
There are 100 hours available in the plant and 75 square metres of vinyl available per operating period.
13. Refer to Figure 25-4. What is the objective function for maximizing profits?
a.
Maximize £15A + £30B
b.
Maximize £50A + £80B
c.
Maximize £35A + £50B
d.
Minimize £15A + £30B
14. Refer to Figure 25-4. The constraint equation representing the materials available for the production
processes is
a.
2A + 4B 100.
b.
16A + 12B = 75.
c.
2A + 4B = 200.
d.
16A + 12B 75.
15. Refer to Figure 25-4. Which of the following statements is INCORRECT?
a.
The materials constraint favours Trailer B over Trailer A.
b.
The time constraint favours Trailer A over Trailer B.
c.
The material constraint favours Trailer A over Trailer B.
d.
The objective function favours Trailer B over Trailer A.
Figure 25-5
The following information is available for Walters Furniture Company, which sells two products:
Table X
Table 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 metres of metal available per operating
period.
16. Refer to Figure 25-5. The constraint equation representing processing time available is
a.
4X + 6Y 200.
b.
4X + 6Y 200.
c.
30X + 18Y 200.
d.
4X + 6Y 400.
17. Refer to Figure 25-5. What is the objective function for maximizing sales?
a.
Maximize 200X + 100Y
b.
Maximize 180X + 90Y
c.
Maximize 50X + 40Y
d.
Minimize 200X + 100Y
18. In the graphic method of solving a linear programming problem, which of the following is depicted on
the graph?
a.
coefficient of correlation
b.
constraint
c.
least-squares line of best fit
d.
break-even point
19. Using the graphic approach to linear programming, the solution is usually
a.
a corner point where two or more constraints intersect.
b.
where the lines intersect farthest from zero.
c.
the point farthest from the Y-axis.
d.
the point farthest from the X-axis.
Figure 25-6
Anderson Company manufactures two different products: A and B. The company has 100 kgs of raw
materials and 300 direct labour-hours available for production.
The time requirements and contribution margins per unit are as follows:
A
B
Raw materials per unit (lbs.)
1
2
Direct-labour hours per unit
4
2
Contribution margin per unit
£4
£5
20. Refer to Figure 25-6. What is the objective function for Anderson Company?
a.
Minimize £4A + £5B.
b.
Maximize £4A + £5B.
c.
Maximize £1A + £2B.
d.
Maximize £4A + £2B.
21. Refer to Figure 25-6. What is the equation for the constraint on raw materials?
a.
£1A + £2B < 100
b.
£4A + £2B < 100
c.
£4A + £5B < 100
d.
£4A + £5B < 300
22. Refer to Figure 25-6. What is the equation for the constraint on direct labour?
a.
£1A + £2B < 300
b.
£4A + £2B < 100
c.
£4A + £5B < 100
d.
£4A + £2B < 300
23. A linear programming model would NOT include which of the following items?
a.
independent variables
b.
constraints
c.
objective function
d.
networks
24. A linear programming problem has an objective function of 10a + 12b. If the optimal solution
provided by the model is to produce and sell 400 units of a and 1,000 units of b, the expected profit is:
a.
£1,400.
b.
£14,800.
c.
£16,000.
d.
£40,800.
Figure 25-7
The following information is available for the Johnson Boat Company, which sells two products:
3- Person Raft
(Variable A)
Kayak
(Variable B)
Selling price
£50
£80
Variable costs
£35
£50
Fixed costs (average)
£10
£20
Processing time
2 hours
4 hours
Vinyl cover used
16 sq. ft.
12sq. ft.
There are 100 hours available in the plant and 75 square metres of vinyl available per operating period.
25. Refer to Figure 25-7. The objective function for this production situation is to:
a.
maximize £15A + £30B.
b.
maximize £50A + £80B.
c.
maximize £35A + £50B.
d.
minimize £15A + £30B.
26. Refer to Figure 25-7. The constraint equation representing the materials available for the production
processes is:
a.
2A + 4B > 100.
b.
16A + 12B = 75.
c.
2A + 4B = 200.
d.
16A + 12B < 75.
27. Refer to Figure 25-7. Which of the following statements is NOT correct?
a.
The materials constraint favours kayaks over rafts.
b.
The time constraint favours rafts over kayaks.
c.
The material constraint favours rafts over kayaks.
d.
The objective function favours kayaks over rafts.
28. A linear programming problem has the following objective function:
20A + 40B + 60C
If the optimal solution provided by the model is to produce and sell 100, 200, and 300 units of A, B,
and C, respectively, what is the expected profit?
a.
£36,000
b.
£120
c.
£24,000
d.
£28,000
PROBLEM
1. Smith Products Ltd.produces two products. The manufacture of these products is partially automated.
Total available labour 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
Labour 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 A that can be produced given the constraints?
d.
What is the optimal solution?
Maximize £5X + £4Y
4X + 2Y 600
2X + 3Y 400
400/2 = 200
600/4 = 150
The machine hour constraint limits production of X to 150 units.
d.
X = 125 units, Y = 50 units.
2. Coffee Ltd.manufactures two different miniature models of furniture, a table and a chair. The company
has 500 metres of lumber, 400 machine hours, and 600 direct labour 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
Metres of lumber per unit
5
2
Machine hours per unit
2
3
Direct labour 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?
3. The Adam Laundry has 200 labour-hours a week available to use in dry cleaning or laundry. Two
thousand cms of hanging space is available. The average item that is dry cleaned takes three cms of
hanging space, whereas laundry items take only 1.5 cms of hanging space. The contribution margin for
laundry items averages £1.75; for dry cleaned items, £3.25. Twenty-five items can be washed per hour,
whereas only 10 can be dry cleaned.
Required:
a.
Determine the objective function. Is it a minimization or maximization function?
b.
Set up the constraint equations.
ANS:
Maximize
£5T + £4C
5T + 2C 500
2T + 3C 400
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) = £533.333
(3)
T = 63.64, C = 90.91
CM = £5(63.64) + £4(90.91) = £681.84
