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 raw material available for production is limited to 160,000 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 80,000 units of Alpha and 60,000 units of Beta. Also assume that the raw material available for production is limited to 160,000 pounds. What total contribution margin will it earn?

15. 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 raw material available for production is limited to 160,000 pounds. If Cane uses its 160,000 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

Answer 1

Computation of contribution margin per pound
Particulars	Alpha	Beta
Selling price per unit	$120.00	$80.00
Variable cost per unit:
Direct material	$30.00	$12.00
Direct labor	$20.00	$15.00
Variable manufacturing overhead	$7.00	$5.00
Variable selling expenses	$12.00	$8.00
Contribution margin per unit	$51.00	$40.00
Raw material required per unit (In pound) (Direct materials/ $6)	5	2
Contribution margin per pound of material	$10.20	$20.00
Rank	2	1

Solution 13:

As raw material quantity is limited, therefore raw material will be utilized first for product providing higher contribution margin per pound. Therefore nos of units of each product to be made to maximize profit;

Beta = 60000 units

Alpha = (160,000 - 60000*2) / 5 = 8000 units

Solution 14:

maximum contribution margin Cane Company can earn given the limited quantity of raw materials = Contribution margin from alpha + Contribution margin from Beta

= (8000 * $51) + (60000*$40)

= $2,808,000

Solution 15:

As current available material is sufficient to meet total demand of Beta product. Therefore extra material will be utilized in production of Alpha Product.

Therefore maximum price that Cane company is willing to pay for additional pound of material = Regular price + Contribution margin per pound of alpha = $6 + $10.20 = $16.20