Short Inc has 5,200 machine hours available each month. The following information on the company's three products is available:

Product 1 Product 2 Product 3

Contribution margin per unit $ 45.00 $ 54.00 $ 22.50

Machine hours per unit 3 2 1

Sales demand in units 900 1,000 3,000

Required:

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

b. What will be the maximum possible contribution margin?

a) Production schedule

Product 3 - 3000 hr * $22.5 = 67,500

Product 2 - 2000 * $ 17/hr = 34,000

Product 1 - - 200 units * $15 / hr = 3,000

b) Possible maximum contribution margin

= $104,500

Explanation:

The production schedule that will be maximize the profit for Short Inc is that which maximizes the contribution per unit if the scarce machine hours.

Since Short Inc faces a limiting a factor in form of machine hours, it should allocate its its resources in such a way that maximises the contribution per unit of machine hours.

This is done below using a table:

Product 1 2 3

Contribution 45.00 54.00 22.50

Machine hour / unit 3 2 1

Contribution per hr 15 17/hr $22.5/hr

Ranking 3rd 2nd 1st

Production schedule:

Prroduct units Machine hours required

3 3000 3000*1 = 3000

2 1000 1000 * 2 = 2000

1 200 66.7 200

5,200

Amount of machine hours available for product 1 is the a balance after allocation to Product 3 and Product 2. It is determined as follows:

=5,200 - (3000 + 2000)

= 200 hours

Units of product 1 to be produced = 200/3 = 66.7 units

Optimum production schedule

Product 3 - 3000 units

Product 2 - 1000 units

Product 1 - -66.7 units

B) Maximum possible contribution margin

Product 3 - 3000 hr * $22.5 = 67,500

Product 2 - 2000 * $ 17/hr = 34,000

Product 1 - - 200 units * $15 / hr = 3,000

Total maximum contribution = $67,500 + $34,000 + $3000

= $104,500