Question

Cane Company manufactures two products called Alpha and Beta that sell for $210 and $172, respectively. Each product uses only one type of raw material that costs $8 per pound. The company has the capacity to annually produce 128,000 units of each product. Its average cost per unit for each product at this level of activity are given below:

	Alpha				Beta
Direct materials		$	40			$	24
Direct labor			38				34
Variable manufacturing overhead			25				23
Traceable fixed manufacturing overhead			33				36
Variable selling expenses			30				26
Common fixed expenses			33				28
Total cost per unit		$	199			$	171

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.

13. Assume that Cane’s customers would buy a maximum of 98,000 units of Alpha and 78,000 units of Beta. Also assume that the company’s raw material available for production is limited to 248,000 pounds. How many units of each product should Cane produce to maximize its profits?

Answer 1

	Alpha	Beta
Sale price	$210	$172
Less: Direct material	40	24
Direct Labor	38	34
Variable manufacturing overhead	25	23
Variable selling expenses	30	26
Contribution margin per unit	$77	$65
Direct material used (pound)	40/8 = 5	24/8 = 3
Contribution margin per pound of raw material	$15.40	$21.67
Rank	2	1

	Alpha	Beta	Total
Material per units (pound)	5	3
Demand	98000	78000
Material needed (pound)	490,000	234,000	724,000
Allocation of material (pound)	14000	234,000	248,000
Divide by Material per units (pound)	5	3
Maximum units to maximize the profit	2,800	78,000