Question

Cane Company manufactures two products called Alpha and Beta that sell for $120 and $80, respectively. Each product uses only one type of raw material that costs $6 per pound. The company has the capacity to annually produce 100,000 units of each product. Its average cost per unit for each product at this level of activity are given below:

	Alpha				Beta
Direct materials		$	30			$	12
Direct labor			20				15
Variable manufacturing overhead			7				5
Traceable fixed manufacturing overhead			16				18
Variable selling expenses			12				8
Common fixed expenses			15				10
Total cost per unit		$	100			$	68

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 80,000 units of Alpha and 60,000 units of Beta. Also assume that the company’s raw material available for production is limited to 160,000 pounds. How many units of each product should Cane produce to maximize its profits?

Answer 1

Calculation of Contribution per unit
	Alpha		Beta
		$        120		$          80
Sale Price Per Unit
Less: Variable Expenses
Direct Materials	$          30		$          12
Direct Labor	$          20		$          15
Variable Manufacturing overhead	$             7		$             5
Variable Selling Expenses	$          12		$             8
Total Variable Expense per unit		$          69		$          40
Contribution Per Unit		$          51		$          40

Calculation of Pound of raw material required per unit of Alpha and Beta
	Alpha	Beta
Per Unit of Direct Material Cost	$          30	$          12
One Pound cost of Raw Material	$             6	$             6
Pound of Material required= Direct Material Cost Per Unit/Per Pound Cost
for Alpha=30/6 =4 pound per unit and for Beta = 12/6 = 2 pound per unit	5 Pound	2 Pound
Calculation of contribution per unit of constrained resource-Raw Material
	Alpha	Beta
Per Unit contribution	$          51	$          40
Pounds of Raw Material required per unit	5	2
Contribution per pound of raw material	$    10.20	$    20.00
Beta has higher contribution per units of constrained resource
So First Maximum units of Beta will be made and from balance raw material Alpha will be made
Total Raw Material Available	160000	Pounds
One Unit of Beta required	2	Pounds
Maximum unit of Beta customer can buy	60000	units
Total Raw material requirement for 60000 units of beta= 60000*2	120000	Pounds
Balance Raw material for Alpha Product = 160000-120000	40000	Pounds
One unit of Alpha Require raw material	5	Pounds
Possible production of Alpha = 40000/5=	8000	units

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