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

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