Question

Cane Company manufactures two products called Alpha and Beta that sell for $215 and $160, respectively. Each product uses only one type of raw material that costs $7 per pound. The company has the capacity to annually produce 125,000 units of each product. Its average cost per unit for each product at this level of activity are given below: Alpha Beta Direct materials $ 42 $ 21 Direct labor 35 28 Variable manufacturing overhead 23 21 Traceable fixed manufacturing overhead 31 34 Variable selling expenses 28 24 Common fixed expenses 31 26 Total cost per unit $ 190 $ 154 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. Cane Company manufactures two products called Alpha and Beta that sell for $215 and $160, respectively. Each product uses only one type of raw material that costs $7 per pound. The company has the capacity to annually produce 125,000 units of each product. Its average cost per unit for each product at this level of activity are given below: Alpha Beta Direct materials $ 42 $ 21 Direct labor 35 28 Variable manufacturing overhead 23 21 Traceable fixed manufacturing overhead 31 34 Variable selling expenses 28 24 Common fixed expenses 31 26 Total cost per unit $ 190 $ 154 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.

11. How many pounds of raw material are needed to make one unit of each of the two products?

12. What contribution margin per pound of raw material is earned by each of the two products? (Round your answers to 2 decimal places.)

13. Assume that Cane’s customers would buy a maximum of 96,000 units of Alpha and 76,000 units of Beta. Also assume that the company’s raw material available for production is limited to 246,000 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 96,000 units of Alpha and 76,000 units of Beta. Also assume that the company’s raw material available for production is limited to 246,000 pounds. What is the maximum contribution margin Cane Company can earn given the limited quantity of raw materials?

15. Assume that Cane’s customers would buy a maximum of 96,000 units of Alpha and 76,000 units of Beta. Also assume that the company’s raw material available for production is limited to 246,000 pounds. If Cane uses its 246,000 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

Cane Company

1. Determination of pounds of raw materials needed to make one unit of each of the two products:

	Alpha	Beta
Direct material cost per unit	$42	$21
raw material cost per pound	$7	$7
pounds per unit	42/7 = 6 pounds	21/7 = 3 pounds

1. Determination of contribution per pound:

• Contribution margin per pound of raw material:

	Alpha	Beta
Selling price per unit	$215	$160
Variable costs per unit:
direct materials	$42	$21
Direct labor	$35	$28
variable manufacturing overhead	$23	$21
variable selling expense	$28	$24
Total variable cost per unit	$128	$94
Contribution margin per unit	$87	$66
direct material cost per pound	$7	$7
number of pounds per unit	6	3
contribution margin per pound	87/6 =$14.50	$22

Ranking                                   II                     I

1. Determination of number of units of each product to be produced to maximize profits:

Since the contribution margin per pound of raw material for Beta is higher than that of Alpha, the limited raw materials of 246,000 pounds should be first used to produce maximum units of Beta.

Maximum demand for Beta = 76,000 units
raw materials needed = 76,000 x 3 = 228,000 pounds

Available raw materials = 246,000 pounds

Remaining raw material in pounds = 246,000 – 228,000 = 18,000 pounds

The number of units of Alpha that can be produced using 18,000 pounds = 18,000/6 = 3,000 units

	Alpha	Beta
sales units	3,000	76,000
contribution margin per unit	$87	$66
total contribution margin	$261,000	$5,016,000	$5,277,000

Hence, the number of units of each product to be produced to maximize profits given the limited quantity of raw materials is Alpha – 3,000 units and Beta – 76,000 units.

The total contribution margin at optimal product mix of Alpha (3,000 units) and Beta (76,000 units) = $5,277,000

1. The total contribution margin the company would earn with limited availability of raw material is $5,277,000 (as computed above).

1. Determination of maximum price for additional pound of raw material:

Since Beta is being allocated adequate raw materials to satisfy its maximum demand, we compute the amount that can be paid per pound for additional raw materials for Alpha –

Cost of raw material per pound = $7

Contribution margin per pound of Alpha = $14.50

Maximum price that can be paid per additional pound of raw material = $7 + $14.50 = $21.50

Hence, the price the company is willing to pay per pound for additional raw material is $21.50.