Question

Betty DeRose, Inc. produces and sells two products, L and V.

Revenue and cost information for the two products from last

month appear below:

Product L Product V

selling price per unit ........... $15.00 $12.00

variable costs per unit .......... $ 8.00 $ 7.00

For the coming month, Betty would like to use linear programming

in order to maximize monthly profits.

Each month Betty has 80,000 direct labor hours available and 60,000

machine hours available. Product L requires 5 direct labor hours for

each unit and 2 machine hours for each unit. Product V requires 4

direct labor hours for each unit and 8 machine hours for each unit.

Calculate the number of units of Product L that should be produced

in order to maximize net income.

Answer 1

Let number of units produced for product L be x and for product V be y.

one unit of x needs 5 labor hours and 2 machine hours.

Similarly, one unit of y needs 4 labor hours and 8 machine hours.

Hence following linear programming equation will be formed, considering the total availability of machine & labor hours:

5x + 4y = 80000 ---equation 1

and

2x + 8y = 60000 ---eq 2

Solving the second equation, 8y = 60000-2x

4y= 30000-x, now putting this value in eq 1

we get, x= 12500 units

Hence, 12500 units will be produced of L for maximum profit.