Question

Benoit Company produces three products—A, B, and C. Data concerning the three products follow (per unit):

	Product
	A				B				C
Selling price	$	80			$	56			$	70
Variable expenses:
Direct materials		24				15				9
Other variable expenses		24				27				40
Total variable expenses		48				42				49
Contribution margin	$	32			$	14			$	21
Contribution margin ratio		40	%			25	%			30	%

The company estimates that it can sell 800 units of each product per month. The same raw material is used in each product. The material costs $3 per pound with a maximum of 5,000 pounds available each month.

What is the maximum contribution margin that the company can earn per month if it makes optimal use of its 5,000 pounds of materials?

Answer 1

• All working forms part of the answer
• Calculation of contribution margin per ‘pound’ of material

Working		A	B	C
A	Direct Material per unit	$24	$15	$9
B	material cost per pound	$3	$3	$3
C= A / B	Pound of material required per unit	8	5	3
D	Contribution margin per unit	$32	$14	$21
E= D / C	Contribution margin per pound of raw material	$4	$2.8	$7
	Order of preference to allocate material	2nd	3rd	1st

Since, Product C has maximum ‘contribution margin per pound’ it will be given 1^st preference, followed by ‘A’ and then ‘B’

• Allocation of available 5000 pounds of raw Material

	A	B	C
Maximum units that can be sold (A)	800	800	800
Material required per unit [in pounds] (B)	8	5	3
Total Material requirement (C) in pounds	6400	4000	2400

Available material in pounds	5000 pounds
(-) First allocation to Product C	2400 pounds
Remaining material	2600 pounds
(-) Second allocation to Product A	2600 pounds
Remaining for Product B	0 pound

• Calculation of total contribution on the basis of above allocation

	A	B	C	Total
Material [in pounds] allocated (A)	2600 pounds	0 pound	2400 pounds	5000 pounds
Contribution per pound (B) [calculated in working above]	$4	$2.8	$7
Total contribution margin (A x B)	$10,400	$0	$16,800	$27,200

Hence, total contribution margin will be $27,200