XYZ Company produces three products, A, B, and C. XYZ's plant capacity is limited to 48,000 machine hours per year. The following information is available for planning purposes: Product A Product B Product C demand for next year ............. 21,000 units 28,000 units 35,000 units selling price per unit ........... $80 $120 $160 direct material cost per unit .... $24 $ 22 $ 36 direct labor cost per unit ....... $18 $ 50 $ 62 variable overhead cost per unit .. $22 $ 25 $ 33 It takes 0.80 machine hours to produce one unit of Product A; 1.20 machine hours to produce one unit of Product B; and 1.60 machine hours to produce one unit of Product C.
Calculate the total number of units of Product B that XYZ Company should produce in order to maximize its net income.

The contribution margin( Sale price - Direct material- direct labor) for product A, B & C per unit is $38, $48 & $ 62 but per hour production( No of units produce is fro product A / hours to produce ) for product A, B & C is 1.3, 0.83 & .63.

Which means in 1 machine we can make contribution margin of $ 47.5 from product A , $ 40 from product B & $38.8 from product C. ( units produced in 1 hour * Per unit Contribution margin.

So, the company should prioritize it's machine hours for product A first than B & C in the last.

The demand for product A is 21,000 units , which means it will require 16,800 hours to meet the demand of product A as 1.3 units can be produced in 1 hour.

Since the total machine hours are 48,000 out of which 16,800 hours have been used for producing product A, so we are left with 31,200 hours while 0.83 units of product B can be produce in an hour. so we can produce 26,000 units of product B to maximize the net income.

Product A Product B Product C Total

Machine Hours 48,000

Demand 21,000 28,000 35,000 84,000

S.P $80.00 $120.00 $160.00

DM $24.00 $22.00 $36.00

DL $18.00 $50.00 $62.00

Contribution Margin Per unit $38.00 $48.00 $62.00

Units Produce Per hour Production 1.3 0.83 0.63