Question

Wasp company produces three products with the following information:

	Product
	A	B	C
Selling price per unit	$17	$19	$26
Variable cost per unit	$8	$10	$12
Machine-hours per unit (MH/unit)	2	3	4

The company has a limit of 13,800 machine-hours available per month and a monthly fixed cost of $4,000. The demand for each of the products is 2,500 units per month.

The company’s goal is to maximize its profitability.

Suppose the company can rent a machine that will provide an additional 1,620 machine-hours per month.

Q.: What is the maximum monthly rent the company should be willing to pay for this machine (assuming they’ve made optimal use of their own machine)?

A.: $   

Answer 1

In the given question we can observe that the Total number of machine hours available to meet its production needs is shorter than the expectation. Therefore, machine hours will be the constraint factor in this problem. Therefore we will determne the optimal product mix that will maximizes the profit of the company.

	Product A	Product B	Product C	Total
a. Number of units produced and sold	2,500	2,500	2,500
b. Machine hours required per unit	2	3	4
c. Total Machine hours required (a * b)	5,000	7,500	10,000	22,500
Total Machine hours available			13,800
Shortage of Machine hours			8,700

Statement showing the Optimal Product Mix:

	Product A	Product B	Product C
a. Number of units produced and sold	2,500	2,500	2,500
b. Selling price per unit	$17	$19	$26
c. Variable Cost per unit	$8	$10	$12
d. Contribution margin per unit (b - c)	$9	$9	$14
e. Machine hours required per unit	2	3	4	13,800 hours
f. Contribution per machine hour (d / e)	$4.50	$3	$3.50
g. Ranking based on highest contribution per machine hour	1	3	2
Units to be produced on the basis of above ranking	2500 units	0	2200 units (8,800 hours / 4)
	5000 hours		(13,800 - 5,000) = 8,800 hours	13,800 hours

Contribution Margin Income statement based on the above optimal mix:

	Product A	Product C	Total
a. Number of units produced and sold	2,500	2,200
b. Contribution margin per unit	$9	$14
c. Total Contribution (a * b)	$22,500	$30,800	$53,300
d. Total Fixed Cost			$4,000
e. Net Operating Income (c - d)		$49,300

If the company has rented a machine which provide an additional 1,620 machine hours then the optimal product mix will be:

	Product A	Product B	Product C	Total
a. Number of units produced and sold	2,500	2,500	2,500
b. Selling price per unit	$17	$19	$26
c. Variable Cost per unit	$8	$10	$12
d. Contribution margin per unit (b - c)	$9	$9	$14
e. Machine hours required per unit	2	3	4	15,420 hours
f. Contribution per machine hour (d / e)	$4.50	$3	$3.50
g. Ranking based on highest contribution per machine hour	1	3	2
Units to be produced on the basis of above ranking	2,500 units	140 units (420 hours / 3)	2,500 units
	5000 hours	(15,420 - 5,000 - 10,000) = 420 hours	10,000 hours	15,420 hours

Contribution Margin Income statement based on the revised optimal mix:

	Product A	Product B	Product C	Total
a. Number of units produced and sold	2,500	140	2,500
b. Contribution margin per unit	$9	$9	$14
c. Total Contribution (a * b)	$22,500	$1,260	$35,000	$58,760
d. Total Fixed Cost				$4000
e. Net Operating Income (c - d)			$54,760

Calculation of maximum amount that can be paid for hiring the machine for addotional hours of 1,620 hours:

	$
a. Net Operating Income without hiring the machine	$49,300
b. Net Operating Income by hiring the machine	$54,760
c. Maximum amount that can be paid for hiring the machine (b - a)	$5,460