Question

Cane Company manufactures two products called Alpha and Beta that sell for $130 and $90, respectively. Each product uses only one type of raw material that costs $5 per pound. The company has the capacity to annually produce 102,000 units of each product. Its average cost per unit for each product at this level of activity are given below:

	alpha	beta
direct materials	$25	$10
direct labor	22	21
variable manufacturing overhead	17	7
traceable fixed manufacturing overhead	18	20
variable selling expenses	14	10
common fixed expenses	17	12
total cost per unit	$113	$80

The company considers its traceable fixed manufacturing overhead to be avoidable, whereas its common fixed expenses are unavoidable and have been allocated to products based on sales dollars.

Questions: (Please show all work/steps)

11. How many pounds of raw material are needed to make one unit of each of the two products?

	alpha	beta
pounds of raw materials per unit	?	?

12. What contribution margin per pound of raw material is earned by each of the two products? (Round your answers to 2 decimal places.

	alpha	beta
contribution margin per pound	?	?

13. Assume that Cane’s customers would buy a maximum of 82,000 units of Alpha and 62,000 units of Beta. Also assume that the company’s raw material available for production is limited to 162,000 pounds. How many units of each product should Cane produce to maximize its profits?

	alpha	beta
units produced	?	?

14. Assume that Cane’s customers would buy a maximum of 82,000 units of Alpha and 62,000 units of Beta. Also assume that the company’s raw material available for production is limited to 162,000 pounds. What is the maximum contribution margin Cane Company can earn given the limited quantity of raw materials?

15. Assume that Cane’s customers would buy a maximum of 82,000 units of Alpha and 62,000 units of Beta. Also assume that the company’s raw material available for production is limited to 162,000 pounds. If Cane uses its 162,000 pounds of raw materials, up to how much should it be willing to pay per pound for additional raw materials? (Round your answer to 2 decimal places.)

Answer 1

Solution 11:

No. of pounds of raw material consumed in Alpha/ Beta can be calculated by dividing the total material cost with Cost per pound

	Alpha	Beta
Direct Material cost per unit	25	10
Material cost per pound	5	5
No. of pounds of raw material consumed	5	2

Solution 12:

For computing contribution margin per pound of raw material earned by each of the two products, we need to calculate the contribution per unit of Alpha and Beta.

	Alpha	Beta
Selling Price	130	90
Less: Variable cost
Direct Material	25	10
Direct Labor	22	21
Variable manufacturing Overhead	17	7
Variable Selling expenses	14	10
Total Variable cost	78	48
Net Contribution per unit	52	42

Contribution per pound of raw material can be calculated as below:

	Alpha	Beta
Net Contribution per unit	52	42
No. of pounds of raw material consumed	5	2
Contribution per pound of raw material	10.4	21

Solution 13:

Since the company’s raw material available for production is limited to 162,000 pounds, it will prioritize that product which is having higher contribution per pound of raw material.

Since Beta is having highest contribution per pound of raw material, company will produce maximum units of beta. Since Beta is having demand of 62,000 units, it will be requiring 124,000 pounds (62,000 *2). Company can easily produce 62,000 units of Beta.

Left over pounds of raw material is 18,000 pounds (162,000 – 124,000). From 38,000 pound of raw material, 7,600 Alpha can be produced (38,000 / 5)

Solution 14: $2,999,200

Maximum contribution will be earned when 62,000 units of Beta will be sold and 7,600 Alpha will be sold (Solution 13)

	Alpha	Beta
No. of units	7,600	62,000
Contribution per unit	52	42
Contribution per pound of raw material	395,200	2,604,000

Total maximum Contribution would be 2,999,200

Solution 15:

Since the demand of Beta is already met, new raw material will be purchased only for Alpha. Since Alpha gives a contribution of $52 per unit, the company can spend a maximum of $52 on variable cost for one unit. Since the company uses 5 pounds of raw material in one unit, it can pay a maximum of additional $10.4 per pound ($52 / 5).

Earlier rate per pound = $5

Additional maximum payment per pound = $10.4

Maximum rate payable per pound = $5 + $10.4= $15.4