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 $ 38 Beta $12 28 Direct materials Direct labor Variable manufacturing overhead Traceable fixed manufacturing overhead Variable selling expenses Common fixed expenses Total cost per unit 16 $100 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. Foundational 11-15 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 places.) Maximum price to be paid per pound $ 15.50

Answer 1

	Alpha	Beta
Pounds per unit ( Direct materials cost per unit / Direct materials cost per pound )	5	2

	Alpha	Beta
Direct materials	30	12
Direct labor	20	15
Variable manufacturing overhead	7	5
Variable selling expenses	12	8
Total variable cost per unit	69	40

	Alpha	Beta
Selling price	120	80
(-) Total variable cost per unit	69	40
Contribution margin per unit	51	40
(/) Pounds per unit	5	2
Contribution margin per pound	10.20	20.00

As the contribution margin per pound of Beta is greater, Cane will produced Beta first and then Alpha
	Alpha	Beta
Pounds per unit	5	2
(*) Demand in units	80000	60000
Total pounds required for production	400000	120000

Pounds of raw materials left after producing Beta = Total raw materials available - Raw materials used for Beta = 160000 - 120000	40000
Units of Alpha that can be produced = Pounds of raw materials left after producing Beta / Pounds per unit of Alpha = 40000 / 5	8000	units

As we can see that with the available raw materials Cane cannot satisfy the demand of Alpha completely.
Maximum price to be paid per pound = Contribution margin per pound of Alpha	10.20