Question

XYZ Company produces three products, A, B, and C. XYZ's plant capacity is
limited to 200,000 machine hours per year. The following information is
available for planning purposes:

                                    Product A       Product B       Product C
demand for next year in units ....  100,000         200,000         150,000
selling price per unit ...........    $18             $28             $24
variable costs per unit ..........    $15             $20             $22

It is known that it takes 0.40 machine hours to produce one unit of Product A;
0.70 machine hours to produce one unit of Product B; and 0.50 machine hours
to produce one unit of Product C.

Calculate the number of units of Product C that XYZ Company should produce
in order to maximize its net income.

Answer 1

XYZ Company must produce the product with highest contribution margin per unit of machine hours in order to maximise net income.

Contribution Margin Per Unit of Machine Hour = Contribution Margin Per unit of Product / Machine Hour per unit of product

A = (18-15) / 0.40 = 7.50

B = (28-20) / 0.70 = 11.43

C = (24-22) / 0.50 = 4

Once it is determined which product maximizes the contribution margin per machine hour, demand should be considered. Often a company can not remain competitive if it totally eliminates one product in order to produce a more profitable product.  

Since, Product B has higher contribution margin per unit of machine hour it will be produced first followed by Product A and then finally Product C depending on machine hours left.

Machine hours for Product B = 200,000 units x 0.70 machine hours per unit = 140,000 machine hours

Machine hours for Product A = 100,000 units x 0.40 machine hours per unit = 40,000 machine hours

Machine hours left = 200,000 - Machine hours for Product A - Machine hours for Product B

Machine hours left = 200,000 - 40,000 - 140,000 = 20,000

So, 20,000 machine hours are remaining for product C which would result in 40,000 units (20,000/0.50)

The number of units of Product C that XYZ Company should produce
in order to maximize its net income is 40,000 units.