Question

Cane Company manufactures two products called Alpha and Beta that sell for $150 and $110, respectively. Each product uses only one type of raw material that costs $5 per pound. The company has the capacity to annually produce 108,000 units of each product. Its unit costs for each product at this level of activity are given below:

  

	Alpha				Beta
Direct materials		$	30			$	15
Direct labor			26				22
Variable manufacturing overhead			13				11
Traceable fixed manufacturing overhead			22				24
Variable selling expenses			18				14
Common fixed expenses			21				16
Total cost per unit		$	130			$	102

  

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

  

Required:

Assume that Cane’s customers would buy a maximum of 86,000 units of Alpha and 66,000 units of Beta. Also assume that the company’s raw material available for production is limited to 210,000 pounds. What is the maximum contribution margin Cane Company can earn given the limited quantity of raw materials?

Answer 1

	Alpha	Beta
Material requirement per unit (Total material cost per unit /cost per pound)	30/5 6 pounds	15/5 = 3 pound

Since Material required for Maximum production of both product is greater than available resource ,Material is a constraint resource.

	Alpha	Beta
selling price	150	110
less:
Direct materials	30	15
Direct labor	26	22
Variable manufacturing overhead	13	11
Variable selling expenses	18	14
Total variable cost	87	62
Contribution margin	63	48
Material requirement per unit	6	3
Contribution per constraint resource	63/6= 10.5	48/3= 16
Ranking based on highest contribution per constraint resource	2	1

Production of Units will be as Follows :

	Number of Units manufactured	Total Material required
Beta	66000	66000*3 pounds = 198000
Alpha	2000	12000          [210000available-198000used]
Total		210000

#Material available for production of Alpha = 210000-198000 =12000 pounds so total number of alpha manufactured = 12000 pounds /6 pounds per unit

= 2000units

	Total contribution
Beta	66000*48= 3168000
Alpha	2000*63= 126000
Total contribution	3,294,000