Question

Use of Limited Resources Northern Production Company has 200 labor-hours available. There is no limit on machine-hours. Northern can sell all of Y it wants, but it can only sell 45 units and 20 units of X and Z, respectively. Product X Product Y Product Z Contribution margin per unit $30 $20 $24 Labor-hours per unit 4 5 4 Required: To maximize profits, how many units of each product should Northern produce?

	Product X	Product Y	Product Z
Contribution margin per unit	$30	$20	$24
Labor-hours per unit	4	5	4

Answer 1

Calculations	Particulars	Product X	Product Y	Product Z
A	Contribution margin per unit	30	20	24
B	Labor-hours per unit	4	5	4
C = A / B	Contribution per labor hour	7.5	4	6
	Ranking	1	3	2

Under the multi-product limited resource allocation, the product giving maximum contribution per unit of limited resource is produced the maximum and then remaining resources are allocated to other products based on ranking

In the present case, labor hours are limited resources and the maximum contribution per unit of limited resource is ranked as Product X, Product Z and lastly Product Y

So, to produce 45 units of product X, labor hours consumed

= Quantity x Labor hour per unit

= 45 x 4

= 180 labor hours

Remaining labor hours

= Total labor hours – consumed labor hours

= 200 – 180

= 20 labor hours

Labor hours required for 20 units of product Z

= 20 x 4

= 80 hours

But hours are limited to 20

So, quantity to be produced of product Z

= Available hours / Hours required per unit

= 20 / 4

= 5 units

Product Y will not be produced as the resources have already been consumed