Question

A firm makes two products, Alpha and Beta.

	Alpha	Beta
Sales price per unit	$7.00	$10.00
Variable cost per unit	$4.00	$8.00
Demand	5,000	4,000
Machine hours used	5	2

The total available machine hours is 10,000.

How many of Alpha should be in the product mix to maximize the profit?

Answer 1

Contribution margin = Sales - Variable cost

Alpha = 7 - 4

= 3

Beta = 10 - 8

= 2

Cintribution per Machine hour = Contribution margin per unit / Machine hour used per unit

Alpha = 3 / 5

= 0.60

Beta = 2 /2

= 1.00

So, The contribution per machine hour is higher for the beta, So, To maximise the profit function we will manufacture the products of beta till the demand exhaust.

Machine Hour used for beta = Machine hour * Number of products/Demand

= 2 * 4000

= 8000

Machine hour left for alpha = 10,000 - 8,000

= 2000

So, Number of Units = Mahcine Hour / Number of mahcine hour per product/ unit

= 2000 / 5

= 400 Units

So, The optimal mix to maiximise the profit is Alpha = 400 Units and Beta = 4000 units