1.
Step 1: Calculate the total cost of making the hinge sets
Direct Material: $2.40
Direct Labor: $3.00
Variable Factory Overhead: $0.80
Fixed Factory Overhead (avoidable): $0.50
Total Unit Cost: $2.40 + $3.00 + $0.80 + $0.50 = $6.70
Quoted Price from Supplier: $7.00
If the company buys the hinge sets, it can lease out the physical space now used to produce
hinges for $360,000 per year.
Make Option
Total Unit Cost: $6.70
Total Cost: $6.70 x 500,000 = $3,350,000
Buy Option
Quoted Price from Supplier: $7.00
Total Cost: $7.00 x 500,000 = $3,500,000
Less: Lease Income: $360,000
Net Cost: $3,500,000 - $360,000 = $3,140,000
Conclusion
Based on the analysis, the company should buy the hinge sets, as it is the more cost-
effective option, saving $210,000 per year ($3,350,000 - $3,140,000).
2.
Step 1: Calculate the incremental revenue from the special order
The special order is for 20,000 units at a price of $9 each.
Incremental Revenue = 20,000 units x $9/unit = $180,000
Step 2: Calculate the incremental cost of the special order
The unit cost information is as follows:
Direct Materials: $3.00
Direct Labor: $2.80
Variable Overhead: $1.50
Total Variable Cost: $3.00 + $2.80 + $1.50 = $7.30
Incremental Cost = 20,000 units x $7.30/unit = $146,000
Step 3: Calculate the incremental profit from the special order
Incremental Profit = Incremental Revenue - Incremental Cost
= $180,000 - $146,000
= $34,000
Step 4: Consider the capacity constraints
The company has a planned production level of 75,000 units and the special order is for
20,000 units. Since the company has excess capacity, accepting the special order will not
affect the production of other units.
Conclusion
Based on the analysis, the company should accept the special order, as it will
generate an incremental profit of $34,000.
3.
Step 1: Determine the contribution margin per unit for each product
Drill:
Sales Price: $80
Variable Cost: $67
Contribution Margin: $80 - $67 = $13
Table Saw:
Sales Price: $120
Variable Cost: $93
Contribution Margin: $120 - $93 = $27
Step 2: Determine the contribution margin per electronic switch for each product
Drill:
Contribution Margin: $13
Electronic Switches per Unit: 1
Contribution Margin per Electronic Switch: $13/1 = $13
Table Saw:
Contribution Margin: $27
Electronic Switches per Unit: 3
Contribution Margin per Electronic Switch: $27/3 = $9
Step 3: Prioritize the product with the highest contribution margin per electronic switch
Since the drill has a higher contribution margin per electronic switch ($13) than the table saw
($9), Landry should prioritize making drills to maximize profit.
Step 4: Determine the number of units per product to be sold
Let's assume x is the number of drills and y is the number of table saws.
The total variable cost is $3,074,000.
The variable cost per drill is $67, and the variable cost per table saw is $93.
We can set up the following equation:
67x + 93y = 3,074,000
We also know that the total number of electronic switches used is 62,000.
Since each drill requires 1 electronic switch and each table saw requires 3 electronic
switches, we can set up the following equation:
x + 3y = 62,000
Step 5: Solve the system of equations
We can solve the system of equations using substitution or elimination.
Let's use substitution.
Rearranging the second equation, we get:
x = 62,000 - 3y
Substituting this expression for x into the first equation, we get:
67(62,000 - 3y) + 93y = 3,074,000
Expanding and simplifying, we get:
4,154,000 - 201y + 93y = 3,074,000
Combine like terms:
-108y = -1,080,000
Divide by -108:
y = 10,000
Now that we have found y, we can find x:
x = 62,000 - 3y
= 62,000 - 3(10,000)
= 62,000 - 30,000
= 32,000
Conclusion
Landry should prioritize making drills to maximize profit.
To achieve the target variable cost of $3,074,000, Landry should produce:
- 32,000 drills
- 10,000 table saws
keep or drop: Norton materials Inc
Step 1: Determine the relevant fixed costs
The relevant fixed costs associated with the roofing tile line are:
- Advertising: $10,000
- Supervision salaries: $35,000
Total relevant fixed costs: $10,000 + $35,000 = $45,000
Step 2: Compare the contribution margin to the relevant fixed costs
Contribution margin: $10,000
Relevant fixed costs: $45,000
Since the relevant fixed costs ($45,000) exceed the contribution margin ($10,000), the
company would incur a net loss of $35,000 if it keeps the segment.
Step 3: Consider the impact of dropping the segment
If the company drops the segment, it will avoid the relevant fixed costs of $45,000.
Conclusion
Based on the analysis, the company should drop the roofing tile segment, as it will result in a
net savings of $35,000.
The company should drop the segment.
Sell or process: apple time
Step 1: Determine the revenue from selling the Grade B apples at split-off
The company can sell 120 five-pound bags of Grade B apples at $1.25 per bag.
Revenue from selling at split-off: 120 bags x $1.25/bag = $150
Step 2: Determine the revenue from processing the Grade B apples into pie fillings
The company can produce 500 cans of pie filling from the Grade B apples.
Revenue from selling pie fillings: 500 cans x $0.90/can = $450
Step 3: Determine the additional costs of processing the Grade B apples into pie fillings
The additional costs of processing the Grade B apples into pie fillings are $0.24 per can.
Total additional costs: 500 cans x $0.24/can = $120
Step 4: Compare the revenue from selling at split-off to the revenue from processing further
Revenue from selling at split-off: $150
Revenue from processing further: $450
Additional costs of processing further: $120
Net revenue from processing further: $450 - $120 = $330
Since the net revenue from processing further ($330) is greater than the revenue from
selling at split-off ($150), the company should process further.
The company should process further.
Optimal product mix
Step 1: Determine the contribution margin per unit of each product
Gear X:
Contribution Margin: $25
Machine Time: 2 hours
Contribution Margin per Machine Hour: $25 / 2 hours = $12.50 per hour
Gear Y:
Contribution Margin: $10
Machine Time: 0.5 hours
Contribution Margin per Machine Hour: $10 / 0.5 hours = $20 per hour
Step 2: Prioritize the product with the highest contribution margin per machine hour
Since Gear Y has a higher contribution margin per machine hour ($20) than Gear X
($12.50), the company should prioritize producing Gear Y.
Step 3: Determine the maximum number of units of Gear Y that can be produced
The company has 40,000 hours of machine time available per year.
Gear Y requires 0.5 hours of machine time per unit.
Maximum number of units of Gear Y: 40,000 hours / 0.5 hours/unit = 80,000 units
However, the company can only sell a maximum of 60,000 units of Gear Y.
Step 4: Determine the remaining machine time available for Gear X
The company will use 60,000 units x 0.5 hours/unit = 30,000 hours to produce Gear Y.
Remaining machine time: 40,000 hours - 30,000 hours = 10,000 hours
Step 5: Determine the number of units of Gear X that can be produced
Gear X requires 2 hours of machine time per unit.
Number of units of Gear X: 10,000 hours / 2 hours/unit = 5,000 units
Conclusion
The company should produce:
- 60,000 units of Gear Y
- 5,000 units of Gear X
The school can sell
Question 1: Should the canteen's management accept the weather forecaster's offer?
Step 1: Calculate the expected contribution margin without the forecast
Probability of hot weather: 65%
Probability of cold weather: 35%
Expected contribution margin from halo-halo: (0.65 x $20,000) + (0.35 x $6,000) = $13,000 +
$2,100 = $15,100
Expected contribution margin from mami: (0.65 x $8,000) + (0.35 x $15,000) = $5,200 +
$5,250 = $10,450
Step 2: Determine the optimal product to sell without the forecast
Since the expected contribution margin from halo-halo ($15,100) is higher than from mami
($10,450), the canteen should sell halo-halo.
Step 3: Calculate the expected value of perfect information
With perfect information, the canteen would sell halo-halo on hot days and mami on cold
days.
Expected value of perfect information: (0.65 x $20,000) + (0.35 x $15,000) = $13,000 +
$5,250 = $18,250
Step 4: Compare the expected value of perfect information to the cost of the forecast
Expected value of perfect information: $18,250
Cost of the forecast: $3,000
Net benefit: $18,250 - $15,100 = $3,150
Since the net benefit ($3,150) is greater than the cost of the forecast ($3,000), the canteen's
management should accept the offer.
Question 2: What is the slack time of the parallel project?
Step 1: Calculate the expected time for the activity
Optimistic time: 3 weeks
Most likely time: 5 weeks
Pessimistic time: 7 weeks
Expected time: (3 + 4 x 5 + 7) / 6 = (3 + 20 + 7) / 6 = 30 / 6 = 5 weeks
Step 2: Calculate the slack time
The parallel project takes 4 weeks to complete.
Slack time: Expected time - Project time = 5 weeks - 4 weeks = 1 week
The slack time is 1 week.
Clients arrive
Step 1: Calculate the average number of clients waiting in line at any time
Arrival rate (λ) = 10 clients per hour
Service rate (μ) = 12 clients per hour
Average number of clients waiting in line (Lq) = λ^2 / (μ(μ-λ))
= 10 / (12-10)
= 10 / 2
= 5 clients
Step 2: Calculate the average number of clients in the waiting line not being serviced
Average number of clients in the system (Ls) = λ / (μ-λ)
= 10^2 / (12(12-10))
= 100 / (12 x 2)
= 100 / 24
= 4.17 clients
Average number of clients being serviced = 1 (since there is only one ATM)
Step 3: Calculate the average waiting time
Average waiting time (Wq) = Lq / λ
= 4.17 clients / 10 clients per hour
= 0.417 hours or 25 minutes
The average number of clients waiting in line at any time is 4.17 clients.
The average number of clients in the waiting line not being serviced is 4 clients.
The average waiting time is 25 minutes.
