Question

Cane company manufactures two products called Alpha and Beta that sell for $135 and $95, respectively. Each product uses only one type of raw material that costs $6 per pound. The company has the capacity to annually produce 105,000 units of each product. Its average cost per unit for each product at this level of activity are given below:
Direct materials 30, 18
Direct labor 23, 16
Variable manufacturing overhead 10, 8
Traceable fixed manufacturing overhead 19, 21
Variable selling expenses 15, 11
Common fixed expenses 18, 13
Total cost per unit 115, 87
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.
1. Assume that Cane's customers would buy a maximum of 83,000 units of Alpha and 63,000 units of Beta. Also assume that the raw material available for production is limited to 200,000 pounds. How many units of each product should Cane produce to maximize its profits?
2. Assume that Cane's customers would buy a maximum of 83,000 units of Alpha and 63,000 units of Beta. Also assume that the raw material available for production is limited to 200,000 pounds. What total contribution margin will it earn?
3. Assume that Cane's customers would buy a maximum of 83,000 units of Alpha and 63,000 units of Beta. Also assume that the raw material available for production is limited to 200,000 pounds. If Cane uses its 200,000 pounds of raw materials, up to how much should it be willing to pay per pound for additional raw materials?

Answer 1

Cane Company

Determination of number of units of each product to be produced to maximize profits given the limited quantity of raw materials:

• Contribution margin per pound of raw material:

	Alpha	Beta
Selling price per unit	$135	$95
Variable costs per unit:
direct materials	$30	$18
Direct labor	$23	$16
variable manufacturing overhead	$10	$8
variable selling expense	$15	$11
Total variable cost per unit	$78	$53
Contribution margin per unit	$57	$42
direct material cost per pound	$6	$6
number of pounds per unit	30/6 = 5	18/6 =3
contribution margin per pound	57/5 =$11.40	42/3 = $14

Ranking                                   II                     I

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

Maximum demand for Beta = 63,000 units
raw materials needed = 63,000 x 3 = 189,000 pounds

Available raw materials = 200,000 pounds

Remaining raw material in pounds = 11,000 pounds

The number of units of Alpha that can be produced using 11,000 pounds = 11,000/5 = 2,200 units

	Alpha	Beta
sales units	2,200	63,000
contribution margin per unit	$57	$42
total contribution margin	$125,400	$2,646,000	$2,771,400

Hence, the number of units of each product to be produced to maximize profits given the limited quantity of raw materials is Alpha – 2,200 units and Beta – 63,000 units. The total contribution margin at optimal product mix of Alpha (2,200 units) and Beta (63,000 units) = $2,771,400

The answer to part 2, the total contribution margin the company would earn with limited availability of raw material is $2,771,400 (as computed above).

1. Determination of the price the company is willing to pay per pound for additional 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 = $6

Contribution margin per pound of Alpha = $11.40

Maximum price that can be paid per additional pound of raw material = $6 + $11.40 = $17.40

Hence, the price the company is willing to pay per pound for additional raw material is $17.40.