Question

The Grand Company produces three products with the followings costs & selling price: \

Product Name Large Medium Small Selling

Price per unit $15 20 20

Variable cost per unit 8 10 12

Machine Hours per unit 3.5 2 2.5

Grand has a limit of 20,000 machine hours available per month. The company has a monthly fixed cost $50,000. If there is virtually unlimited demande for each of the products, what is the maximum monthly profit? If the demand for each of the products is 3000 units per month what is the maximum monthly contribution margin that can be realized by the company.

Answer 1

	Large	Medium	Small
Selling price per unit	15	20	20
Variable cost per unit	-8	-10	-12
Contribution Margin per unit	7	10	8
Machine hours per unit	3.5	2	2.5
Contribution margin per machine hour	7/3.5 = $2	10/2 =$5	8/2.5=$3.2

(i) If there is virtually unlimited demand for each product, all machine hours should be used for production of product Medium since it has highest contribution margin per machine hour.

Maximum output of product medium = Machine hours available / Machine hours per unit

= 20,000/2

= 10,000 units

Contribution margin ( 10,000 x 10)	100,000
Fixed cost	-50,000
Profit	$50,000

Hence, maximum profit = $50,000

(ii) If demand is restricted to 3,000 units per month for each product, available machine hours should be used first, for the production of product medium , then for the production of product small and finally remaining machine hours should be used for the production of product large.

Output Schedule
	Medium	Small	Large
Output	3,000	3,000	1,857
Machine hours per unit	2	2.5	3.5
Machine hours used	6,000	7,500	6,500

	Large	Medium	Small
Units	1,857	3,000	3,000
Contribution margin per unit	$7	$10	$8
Total Contribution Margin	$12,999	$30,000	$24,000

Maximum monthly contribution margin = 12,999+30,000+24,000

= $66,999