Question

Betty DeRose, Inc. produces and sells two products, L and V. Last month, Betty produced and sold 6,000 units of Product L and 4,000 units of Product V. Cost and revenue information for the two products from last month appears below: selling price per unit ........... variable costs per unit .......... Product L $8.00 $3.00 Product V $9.00 $5.00 For the coming month, Betty would like to use linear programming in order to maximize monthly profits. Each month Betty has 60,000 direct labor hours available and 80,000 machine hours available. Product L requires 4 direct labor hours for each unit and 8 machine hours for each unit. Product V requires 6 direct labor hours for each unit and 4 machine hours for each unit. Calculate the number of units of Product V that should be produced in order to maximize net income.

Answer 1

	L	V
Selling Price per unit (A)	8	9
Variable cost per unit (B)	3	5
Contribution per unit (C = A-B)	5	4

Let 'L' be the units of Product L, and'

'V' be the product V

So,

Maximize Z = 5L + 4V

Subject to,

8L + 4V <= 80000 (ie., MH) ...(1)

4L + 6V <=60000 (ie., DLH) ...(2)

L,V <=0

Solving (1) and (2) we get,

L = 7500 units and V = 5000 Units.

So 7500 units of V to be produced to maximise the profits.

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