Question

ABC Company produces Product X, Product Y, and Product Z. All three products require processing on specialized finishing machines. The capacity of these machines is 1,200 hours per month. ABC Company wishes to determine the product mix that should be achieved to meet the high demand for each product and provide the maximum profit. Following is information about each product: Product X Product Y Product Z Selling Price $100 $80 $25 Variable Costs 70 40 20 Machine time per unit 3 hours 2 hours 1 hour Monthly demand (units) 300 200 500 Determine how the 1200 hours of machine time should be allocated to the three products to provide the most profitable product mix. Product X = _____ hours Product Y = _____ hours Product Z = ______ hours

Answer 1

400; 800

Step-by-step explanation:

Contribution:

Product X:

= Selling price - Variable cost

= 100 - 70

= 30,

Product Y:

= Selling price - Variable cost

= 80 - 40

= 40,

Product Z:

= Selling price - Variable cost

= 25 - 20

= 5

Machine hours required :

Product X:

= Machine time per unit × Monthly demand

= 3 × 300

= 900,

Product Y:

= Machine time per unit × Monthly demand

= 2 × 200

= 400,

Product Z:

= Machine time per unit × Monthly demand

= 1 × 500

= 500

Contribution per machine hour:

Product X = Contribution ÷ Machine time per unit

= 30 ÷ 3

= 10,

Product Y = Contribution ÷ Machine time per unit

= 40 ÷ 2

= 20,

Product Z = Contribution ÷ Machine time per unit

= 5 ÷ 1

= 5

It is highest for Y, so produce maximum amount of Y, then X and then Z

Y needs 400 hrs, we are left with 800 hours, so produce 800 hours of X.