Toledo Manufacturing Ltd., produces three products: X, Y, and Z. A limitation of
ID: 2740652 • Letter: T
Question
Toledo Manufacturing Ltd., produces three products: X, Y, and Z. A limitation of 240 labor hours per week prevents the company from meeting the sales demand for these products. Product information is as follows: ............
X.................. .............Y............................... Z
Unit Selling Price:...........................................................160 ............................100............................ 210 Unit Variable Costs:....................................................... (100)........................... (50)........................... (180) Unit Contribution Margin:................................................. 60.............................. 50.............................. 30 Labor Hours per Unit:....................................................... 6................................ 4............................... 6
a) Determine the weekly contribution from each product when total labor hours are allocated to the product with the highest:
1. Unit Selling Price
2. Unit Contribution Margin
3. Contribution per Labor Hour (Hint: each simulation is independent of the others)
b) What generalizations can be made regarding the allocation of limited resources to achieve short-run profit maximization?
c) Determine the opportunity costs the company will incur if management requires the weekly production of 12 units of Z.
d) Give reasons why a company may not allocate resources in the most economical way in some situations.
Explanation / Answer
Step-1: Collecting the information which was provided:
Details
X
Y
Z
Unit selling price
160
100
210
Unit variable cost
(100)
(50)
(180)
Unit contribution margin
60
50
30
Labor Hours per Unit
6
4
6
a) Determine the weekly contribution from each product when total labor hours are allocated to the product with the highest:
1. Unit Selling Price:
Here, based on the unit selling price the highest price is $210 of product Z
units to be produced = 240hours / 6hours per unit = 240 / 6hours = 40units
Therefore, contribution for 40 units = 30per unit * 40units = $1,200
2. Unit Contribution Margin:
Here, based on the unit selling price the highest price is $60per unit of product X
units to be produced = 240hours / 6hours per unit = 240 / 6hours = 40units
Therefore, contribution for 40 units = 60per unit * 40units = $2,400
3. Contribution per Labor Hour:
Details
X
Y
Z
Contribution
60
50
30
Labor hours per unit
6
4
6
Contribution per labor = contribution / labor hour per unit
60/6 = 10
50/4 =12.5
30/6 = 5
Ranking based on Contribution per labor hour
2nd
1st
3th
So, based on above ranking we will select product Y for allocating labor hours,
units to be produced = 240hours / 4hours per unit = 240 / 4hours = 60units
Therefore, contribution for 40 units = 60per unit * 50units = $3,000
b) What generalizations can be made regarding the allocation of limited resources to achieve short-run profit maximization?
For short-run profit maximization, product mix should be in the presence of resource constrain (here it is labor hour). For this purpose it is necessary to allocate available labor hours on the basis of the contribution margins expressed on a per-labor-hour basis. In the present case, Product Y has the highest ranking we will allocation complete labor hours to product Y.
Toledo Manufacturing Ltd. is the more profitable of the product when measured on this basis. Thus, labor hours should be devoted to the production of this product up to whatever is needed to meet weekly demand.
Based on the demand first they need to produce product Y, any remaining labor hours should be used to produce next product X and finally product Z.
c) Determine the opportunity costs the company will incur if management requires the weekly production of 12 units of Z.
computation of opportunity cost:
If management want to produce 12units of product Z, that means 12units * 6 hours per unit = 72 hours are required
that equals to 72hours / 4hors per unit of product Y = 18units of product Y
Therefore, contribution forgone = 18units * 50contribution per unit = $900
The opportunity cost the company will incur = contribution forgone by product Y - contribution from product Z
= $900 - 12units *30 = 900 - 360 = $540 is the opportunity cost
d) Give reasons why a company may not allocate resources in the most economical way in some situations.
Here, this problem has a single constraint that is labor hours. To achieve short-run profit maximization, a company should allocate limited resources in a manner that maximizes the contribution per unit of the limited resource.
Product Z has the highest selling price and Product X has the highest unit contribution margin. Product Y is showing the highest contribution per hour. (based on the above calculations)
Despite this analysis, management may decide on a product mix that includes some units of X or Z or both to satisfy the requests of some “good” customers or to offer a full product line. However, such decisions sacrifice short-run profits.
Details
X
Y
Z
Unit selling price
160
100
210
Unit variable cost
(100)
(50)
(180)
Unit contribution margin
60
50
30
Labor Hours per Unit
6
4
6