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?

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