SOLUTION
1.
A110
B382
C657
Selling price
$168
$ 112
$140
Variable costs:
Direct materials (DM)
48
30
18
Labor and other costs
56
54
80
Total variable costs
104
84
98
Contribution margin
$ 64
$ 28
$ 42
Pounds of DM per unit
÷8 lbs.
÷5 lbs.
÷ 3 lbs.
Contribution margin per lb.
$ 8 per lb.
$5.60 per lb.
$ 14 per lb.
First, satisfy minimum requirements.
A110
C657
Total
Minimum units
200
200
Times pounds per unit
×8 lb. per unit
×5 lb. per unit
×3 lb. per unit
Pounds needed to produce minimum units
1,600 lb.
600 lb.
3,200 lb.
The remaining 1,800 pounds (5,000 – 3,200) should be devoted to C657 because it has the highest
contribution margin per pound of direct material. Because each unit of C657 requires 3 pounds of
Voxx, the remaining 1,800 pounds can be used to produce another 600 units of C657. The
following combination yields the highest contribution margin given the 5,000 pounds constraint
on availability of Voxx.
A110: 200 units
B382: 200 units
C657: 800 units (200 minimum + 600 extra)
2. The demand for Wechsler’s products exceeds the materials available. Assuming that fixed costs
are covered by the original product mix, Wechsler would be willing to pay up to an additional $14
per pound (the contribution margin per pound of C657) for another 1,200 pounds of Voxx. That
is, Wechsler would be willing to pay $6 + $14 = $20 per pound of Voxx for the pounds of Voxx
that will be used to produce C657.1 If sufficient demand does not exist for 400 units (1,200 pounds
÷ 3 pounds per unit) of C657, then the maximum price Wechsler would be willing to pay is an
additional $8 per pound (the contribution margin per pound of A110) for the pounds of Wechsler
that will be used to produce A110. In this case Wechsler would be willing to pay $6 + $8 = $14
pound. If all the 1,200 pounds of Voxx are not used to satisfy the demand for C657 and A110, then
the maximum price Wechsler would be willing to pay is an additional $5.60 per pound (the
contribution margin per pound of B382) for the pounds of Voxx that will be used to produce B382.
Wechsler would be willing to pay $5.60 + $6 = $11.60 per pound of Voxx.
1An alternative calculation focuses on column 3 for C657 of the table in requirement 1.
Selling price
$140
Variable labor and other costs (excluding direct materials)
80
Contribution margin
$ 60
Divided by pounds of direct material per unit
÷3 lbs.
Direct material cost per pound that Wechsler can pay
without contribution margin becoming negative
$ 20
11-38 (30–40 min.) Product mix, relevant costs.
(N. Melumad, adapted) Gormley Precision Tools makes cutting tools for metalworking operations.
It makes two types of tools: A6, a regular cutting tool, and EX4, a high–precision cutting tool. A6
is manufactured on a regular machine, but EX4 must be manufactured on both the regular machine
and a high-precision machine. The following information is available:
Additional information includes the following:
a. Gormley faces a capacity constraint on the regular machine of 50,000 hours per year.
b. The capacity of the high-precision machine is not a constraint.
c. Of the $1,100,000 budgeted fixed overhead costs of EX4, $600,000 are lease payments for the
high-precision machine. This cost is charged entirely to EX4 because Gormley uses the
machine exclusively to produce EX4. The company can cancel the lease agreement for the
high-precision machine at any time without penalties.
d. All other overhead costs are fixed and cannot be changed.
Required:
1. What product mix—that is, how many units of A6 and EX4—will maximize Gormley’s
operating income? Show your calculations.
2. Suppose Gormley can increase the annual capacity of its regular machines by 15,000 machine-
hours at a cost of $300,000. Should Gormley increase the capacity of the regular machines by
15,000 machine-hours? By how much will Gormley’s operating income increase or decrease?
Show your calculations.
3. Suppose that the capacity of the regular machines has been increased to 65,000 hours. Gormley
has been approached by Clark Corporation to supply 20,000 units of another cutting tool, V2,
for $240 per unit. Gormley must either accept the order for all 20,000 units or reject it totally.
V2 is exactly like A6 except that its variable manufacturing cost is $140 per unit. (It takes 1
hour to produce one unit of V2 on the regular machine, and variable marketing cost equals $30
per unit.) What product mix should Gormley choose to maximize operating income? Show
your calculations.
SOLUTION
1.
A6
EX4
Selling price
$ 200
$ 300
11-3
Variable manufacturing cost per unit
120
200
Variable marketing cost per unit
30
70
Total variable costs per unit
150
270
Contribution margin per unit
$ 50
$ 30
Contribution margin per hour of the
constrained resource
$50
1
= $50
$30
0.5
= $60
Total contribution margin from selling only A6
or only EX4
A6: $50 50,000; EX4: $60 50,000
$2,500,000
$3,000,000
Less Lease costs of high-precision machine
to produce and sell EX4
0
600,000
Net relevant benefit
$2,500,000
$2,400,000
Even though EX4 has the higher contribution margin per unit of the constrained resource, the fact
that Gormley must incur additional costs of $600,000 to achieve this higher contribution margin
means that Gormley is better off using its entire 50,000–hour capacity on the regular machine to
produce and sell 50,000 units (50,000 hours 1 hour per unit) of A6. The additional contribution
from selling EX4 rather than A6 is $500,000 ($3,000,000 − $2,500,000), which is not enough to
cover the additional costs of leasing the high–precision machine. Note that, because all other
overhead costs are fixed and cannot be changed, they are irrelevant for the decision. Gormley
produces 50,000 units of A6, which increases operating income by $2,500,000.
2. If capacity of the regular machines is increased by 15,000 machine-hours to 65,000
machine-hours (50,000 originally + 15,000 new), the net relevant benefit from producing A6 and
EX4 is as follows:
A6 EX4
Total contribution margin from selling only
A6 or only EX4
A6: $50 65,000; EX4: $60 65,000 $3,250,000 $3,900,000
Less Lease costs of high–precision machine
that would be incurred if EX4 is produced and sold 600,000
Less Cost of increasing capacity by
15,000 hours on regular machine 300,000 300,000
Net relevant benefit $2,950,000 $3,000,000
Adding 15,000 machine-hours of capacity for regular machines and using all the capacity to
produce EX4 increases operating income by $3,000,000.
Investing in the additional capacity increases Gormley’s operating income by $500,000
($3,000,000 calculated in requirement 2 minus $2,500,000 calculated in requirement 1), so
Gormley should add 15,000 hours to the regular machine. With the extra capacity available to it,
Gormley should use its entire capacity to produce EX4. Using all 65,000 hours of capacity to
produce EX4 rather than to produce A6 generates additional contribution margin of $650,000
($3,900,000 − $3,250,000), which is more than the additional cost of $600,000 to lease the high–
11-4
precision machine. Gormley should therefore produce and sell 130,000 units of EX4 (65,000 hours
0.5 hours per unit of EX4) and zero units of A6.
3. A6 EX4 V2
Selling price $200 $300 $240
Variable manufacturing costs per unit 120 200 140
Variable marketing costs per unit 30 70 30
Total variable costs per unit 150 270 170
Contribution margin per unit $ 50 $ 30 $ 70
Contribution margin per unit of the constrained resource
$50
1
= $50;
$30
0.5
= $60;
$70
1
= $70
The first step is to compare the operating profits that Gormley could earn if it accepted the
Clark Corporation offer for 20,000 units with the operating profits Gormley is currently
earning. V2 has the highest contribution margin per hour on the regular machine and requires
no additional investment such as leasing a high–precision machine. To produce the 20,000
units of V2 requested by Clark Corporation, Gormley would require 20,000 hours on the
regular machine resulting in contribution margin of $70 20,000 = $1,400,000.
Gormley now has 45,000 hours available on the regular machine to produce A6 or EX4.
A6 EX4
Total contribution margin from selling only
A6 or only EX4
A6: $50 45,000; EX4: $60 45,000 $2,250,000 $2,700,000
Less Lease costs of high–precision machine
to produce and sell EX4 − 600,000
Net relevant benefit $2,250,000 $2,100,000
Gormley should use all the 45,000 hours of available capacity to produce 45,000 units of A6.
Thus, the product mix that maximizes operating income is 20,000 units of V2, 45,000 units of A6,
and zero units of EX4. This optimal mix results in a contribution margin of $3,650,000 ($1,400,000
from V2 and $2,250,000 from A6). Relative to requirement 2, operating income increases by
$650,000 ($3,650,000 minus $3,000,000 calculated in requirement 2). Hence, Gormley should
accept the Clark Corporation business and supply 20,000 units of V2.
11-39 (20 min.) Theory of constraints, throughput contribution, relevant costs.
Nebraska Industries manufactures electronic testing equipment. Nebraska also installs the
equipment at customers’ sites and ensures that it functions smoothly. Additional information on
the manufacturing and installation departments is as follows (capacities are expressed in terms of
the number of units of electronic testing equipment):
11-5
Nebraska manufactures only 275 units per year because the installation department has only
enough capacity to install 275 units. The equipment sells for $45,000 per unit (installed) and has
direct material costs of $20,000. All costs other than direct material costs are fixed. The following
requirements refer only to the preceding data. There is no connection between the requirements.
Required:
1. Nebraska’s engineers have found a way to reduce equipment manufacturing time. The new
method would cost an additional $50 per unit and would allow Nebraska to manufacture 20
additional units a year. Should Nebraska implement the new method? Show your calculations.
2. Nebraska’s designers have proposed a change in direct materials that would increase direct
material costs by $2,000 per unit. This change would enable Nebraska to install 310 units of
equipment each year. If Nebraska makes the change, it will implement the new design on all
equipment sold. Should Nebraska use the new design? Show your calculations.
3. A new installation technique has been developed that will enable Nebraska’s engineers to
install 7 additional units of equipment a year. The new method will increase installation costs
by $55,000 each year. Should Nebraska implement the new technique? Show your
calculations.
4. Nebraska is considering how to motivate workers to improve their productivity (output per
hour). One proposal is to evaluate and compensate workers in the manufacturing and
installation departments on the basis of their productivities. Do you think the new proposal is
a good idea? Explain briefly.
SOLUTION
1. It will cost Nebraska $50 per unit to reduce manufacturing time. But manufacturing is not
a bottleneck operation; installation is. Therefore, manufacturing more equipment will not increase
sales and throughput margin. Nebraska Industries should not implement the new manufacturing
method.
2. Increase in throughput margin, $25,000 5 units, $ 875,000
Additional relevant costs of new direct materials, $2,000 310 units, 620,000
Increase/(Decrease) in operating income $ 255,000
The additional incremental costs exceed the benefits from higher throughput margin by $90,000,
so Nebraska Industries should not implement the new design.
Alternatively, compare throughput margin under each alternative.
With the modification, throughput margin is $23,000  $7,130,000
Current throughput margin is $25,000 275 6,875,000
Increase/(Decrease) in operating income $ 255,000
11-6
The throughput margin resulting from the proposed change in direct materials is greater than the
current throughput margin. Therefore, Nebraska Industries should implement the new design.
3. Increase in throughput margin, $25,000 units $ 175,000
Increase in relevant costs 55,000
Increase in operating income $ 120,000
The additional throughput margin exceeds incremental costs by $120,000, so Nebraska Industries
should implement the new installation technique.
4. Motivating installation workers to increase productivity is worthwhile because installation
is a bottleneck operation, and any increase in productivity at the bottleneck will increase
throughput margin. On the other hand, motivating workers in the manufacturing department to
increase productivity is not worthwhile. Manufacturing is not a bottleneck operation, so any
increase in output will result only in extra inventory of equipment. Nebraska Industries should
encourage manufacturing to produce only as much equipment as the installation department needs,
not to produce as much as it can. Under these circumstances, it would not be a good idea to evaluate
and compensate manufacturing workers on the basis of their productivity.
11-40 (30-35 min.) Theory of constraints, contribution margin, sensitivity analysis.
Talking Toys (TT) produces dolls in two processes: molding and assembly. TT is currently
producing two models: Chatty Chelsey and Talking Tanya. Production in the molding department
is limited by the amount of materials available. Production in the assembly department is limited
by the amount of trained labor available. The only variable costs are materials in the molding
department and labor in the assembly department. Following are the requirements and limitations
by doll model and department:
The following requirements refer only to the preceding data. There is no connection between the
requirements.
Required:
1. If there were enough demand for either doll, which doll would TT produce? How many of
these dolls would it make and sell?
2. If TT sells three Chatty Chelseys for each Talking Tanya, how many dolls of each type would
it produce and sell? What would be the total contribution margin?
11-7
3. If TT sells three Chatty Chelseys for each Talking Tanya, how much would production and
contribution margin increase if the molding department could buy 900 more pounds of
materials for $8 per pound?
4. If TT sells three Chatty Chelseys for each Talking Tanya, how much would production and
contribution margin increase if the assembly department could get 65 more labor hours at $12
per hour?
SOLUTION
1. Assuming only one type of doll is produced, the maximum production in each department
given their resource constraints is:
Molding
Department
Assembly
Department
Contribution Margin
Chatty Chelsey
36,000 lbs = 18,000
2 lbs
8,500 hours = 34,000
1/4 hours
$39 − 2 × $8 – 1/4 × $12
= $20
Talking Tanya
36,000 lbs = 12,000
3 lbs
8,500 hours = 25,500
1/3hours
$50 − 3 × $8 – 1/3 × $12
= $22
For both types of dolls, the constraining resource is the availability of material because this
constraint causes the lowest maximum production.
If only Chatty Chelsey is produced, TT can produce 18,000 dolls with a contribution margin of
18,000 × $20 = $360,000
If only Talking Tanya is produced, TT can produce 12,000 dolls with a contribution margin of
12,000 × $22 = $264,000.
TT should produce Chatty Chelseys.
2. As shown in Requirement 1, available material in the Molding department is the limiting
constraint.
If TT sells three Chatty Chelseys for each Talking Tanya, then the maximum number of Talking
Tanya dolls the Molding Department can produce (where the number of Talking Tanya dolls is
denoted as T) is:
(T × 3 lbs.) + ([3 × T] × 2 lbs.) = 36,000 lbs.
3T + 6T = 36,000
9T = 36,000
T = 4,000
The Molding Department can produce 4,000 Talking Tanya dolls, and 3 × 4,000
(or 12,000) Chatty Chelsey dolls.
Because TT can only produce 4,000 Talking Tanyas and 12,000 Chatty Chelseys before it runs
out of ingredients, the maximum contribution margin (CM) is:
Contribution margin
from Chatty Chelsey
+
Contribution margin
from Talking Tanya
= 12,000 × $20 + 4,000 × $22
= $240,000 + 88,000
= $328,000
11-9
3. With 900 more pounds of materials, TT would produce more dolls. Using the same
technique as in Requirement 2, the increase in production is:
(T × 3 lbs.) + ([2 × T] × 2 lbs.) = 900 lbs.
3T + 6T = 900
T = 100
TT would produce 100 extra Talking Tanya dolls and 300 extra Chatty Chelsey dolls.
Contribution margin would increase by
Contribution margin
from Chatty Chelsey
+
Contribution margin
from Talking Tanya
= 300 $20 + 100 $22
= $6,000 + $2,200
= $8,200
4. With 65 more labor hours, production would not change. The limiting constraint is
pounds of material, not labor hours. TT already has more labor hours available than it needs.
11-41 (25 min.) Closing down divisions.
Ainsley Corporation has four operating divisions. The budgeted revenues and expenses for each
division for 2014 follows:
Further analysis of costs reveals the following percentages of variable costs in each division:
Closing down any division would result in savings of 40% of the fixed costs of that division.
Top management is very concerned about the unprofitable divisions (A and B) and is
considering closing them for the year.
Required:
1. Calculate the increase or decrease in operating income if Ainsley closes division A.
2. Calculate the increase or decrease in operating income if Ainsley closes division B.
3. What other factors should the top management of Ainsley consider before making a decision?