Question

Short Inc has 6,000 machine hours available each month. The following information on the company's three products is available:

	Product 1				Product 2				Product 3
Selling price	$	90.00				80.00				50.00
Variable cost per unit		30.00				54.00			$	26.00
Machine hours per unit		5				2				1.5
Sales demand in units		500				1,000				2,000

Required:
a. What production schedule will maximize the company's profits?

b. What will be the maximum possible contribution margin?

c. The company has an option of buying an additional machine for $55,000 to increase the total machine hours to 8,000. Assuming that this machine will last for 3 years and have no resale value at the end of its life, should the company buy this machine?

Answer 1

a.

	Product 1	Product 2	Product 3
Selling Price per Unit	$ 90	$ 80	$ 50
Variable Cost per Unit	30	54	26
Contribution Margin per Unit	$ 60	$ 26	$ 24
Machine Hours per Unit	5	2	1.5
Contribution Margin per Machine Hour	$ 12	$ 13	$ 16
Rank	3	2	1

Production Schedule:

Total Machine Hours	6,000
Less : Utilized for total sales demand of Product 3 ( 2,000 x 1.5)	(3,000)
Less: Utilized for total sales demand of Product 2 ( 1,000 x 2)	(2,000)
Remaining Machine Hours for Product 1	1,000
Number of units of Product 1 than can be produced ( 1,000 MH / 5 MH per unit)	200

Product 1 : 200 units, Product 2 : 1,000 units, Product 3 : 2,000 units.

b. Maximum possible contribution margin per month = 2,000 x $ 24 + 1,000 x $ 26 + 200 x $ 60 = $ 86,000.

c. Contribution margin per month after enhanced capacity = 2,000 x $ 24 + 1,000 x $ 26 + 500 x $ 60 = $ 104,000.

Increase in contribution margin per month = $ 104,000 - $ 86,000 = $ 18,000.

Additional fixed cost ( depreciation on new equipment) = $ 55,000 / 36 months = $ 1,528.

Increase in operating income after purchase of equipment = $ 18,000 - $ 1,528 = $ 16,472 per month.

Therefore, the company should buy the machine, as that would result in increased operating income of $ 16,472 per month. Moreover, it would ensure that the company isable to cater to the total demand for each of its products, as the resource constraint ( Machine Hours) will be taken care of .