Question

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Cane Company manufactures two products called Alpha and Beta that sell for $205 and $164, respectively. Each product uses only one type of raw material that costs $8 per pound. The company has the capacity to annually produce 127,000 units of each product. Its average cost per unit for each product at this level of activity are given below:

	Alpha				Beta
Direct materials		$	40			$	24
Direct labor			37				30
Variable manufacturing overhead			24				22
Traceable fixed manufacturing overhead			32				35
Variable selling expenses			29				25
Common fixed expenses			32				27
Total cost per unit		$	194			$	163

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 97,000 units of Alpha and 77,000 units of Beta. Also assume that the raw material available for production is limited to 247,000 pounds. How many units of each product should Cane produce to maximize its profits?

14. Assume that Cane’s customers would buy a maximum of 97,000 units of Alpha and 77,000 units of Beta. Also assume that the raw material available for production is limited to 247,000 pounds. What total contribution margin will it earn?

15. Assume that Cane’s customers would buy a maximum of 97,000 units of Alpha and 77,000 units of Beta. Also assume that the raw material available for production is limited to 247,000 pounds. If Cane uses its 247,000 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.)

Answer 1

	Alpha	Beta
Pounds of raw materials per unit ( Direct materials cost per unit / Direct materials cost per pound )	5	3

	Alpha	Beta
Direct materials	40	24
Direct labor	37	30
Variable manufacturing overhead	24	22
Variable selling expenses	29	25
Total variable cost per unit	130	101
	Alpha	Beta
Selling price	205	164
(-) Total variable cost per unit	130	101
Contribution margin per unit	75	63
(/) Pounds per unit	5	3
Contribution margin per pound	15.00	21.00

13.

As the contribution margin per pound of Beta is greater, Cane will produced Beta first and then Alpha

	Alpha	Beta
Pounds per unit	5	3
(*) Demand in units	97000	77000
Total pounds required for production	485000	231000
Pounds of raw materials left after producing Beta = Total raw materials available - Raw materials used for Beta = 247000 - 231000	16000
Units of Alpha that can be produced = Pounds of raw materials left after producing Beta / Pounds per unit of Alpha = 16000 / 5	3200	units

	Alpha	Beta
Units produced	3200	77000

14.
Total contribution margin = ( Units of Alpha * Contribution margin per unit ) + ( Units of Beta * Contribution margin per unit ) = ( 3200 * 15 ) + ( 77000 * 21 )	1665000

15.
As we can see that with the available raw materials Cane cannot satisfy the demand of Alpha completely.
Selling price per unit of Alpha	205
(-) Direct labor of Alpha	37
(-) Variable manufacturing overhead of Alpha	24
(-) Variable selling expense of Alpha	29
Maximum Cost of direct materials to be paid per unit	115
(/) Pounds of raw materials per unit of Alpha	5
Maximum price to be paid per pound	23.00