Question

Cane Company manufactures two products called Alpha and Beta that sell for $155 and $115, respectively. Each product uses only one type of raw material that costs $6 per pound. The company has the capacity to annually produce 110,000 units of each product. Its average cost per unit for each product at this level of activity are given below:

	Alpha				Beta
Direct materials		$	24			$	12
Direct labor			23				26
Variable manufacturing overhead			22				12
Traceable fixed manufacturing overhead			23				25
Variable selling expenses			19				15
Common fixed expenses			22				17
Total cost per unit		$	133			$	107

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 87,000 units of Alpha and 67,000 units of Beta. Also assume that the raw material available for production is limited to 168,000 pounds. How many units of each product should Cane produce to maximize its profits?

Alpha:

Beta:

Answer 1

SOLUTION:

Particulars	Alpha	Beta
Selling price per unit (A)	155	115
Variable costs
Direct materials	24	12
Direct labor	23	26
Variable manufacturing overhead	22	12
Variable selling expenses	19	15
Total variable cost per unit (B)	88	65
Contribution margin per unit (C=A-B)	67	50
Pounds of raw materials per unit	4 (24/6)	2(12/6)
Contribution margin per pound of raw material	$ 16.75 (67/4)	$ 25 (50/2)

Beta should be emphasized over Alpha in production, because the contribution margin per pound of raw material is higher for Beta,

Maximum demand of Beta is 67,000.

Raw materials required for 67,000 units of beta = 67,000 x 2

= 134,000 pounds.

Limited Raw Materials (A)	168,000 pounds
Utilized for Beta (B)	134,000 pounds
Available for Alpha (A-B)	34,000 pounds

The output of Alpha = 34,000 / 4 = 8,500 units.

Therefore, in order to maximize profits,

Cane should produce 67,000 units of Beta and 8,500 units of Alpha