Question

A company produces mixers and food processor. Profit on selling one mixer and one food processor is Rs 2,000 and Rs 3,000 respectively. Both the products are processed through three machines A, B, C. The time required in hours for each product and total time available in hours per week on each machine arc as follows:

Machine	Mixer	Food Processor	Available time
A	3	3	36
B	5	2	50
C	2	6	60

Formulate the problem as L.P.P. in order to maximize the profit.

Answer 1

Let x = number of mixers are sold
      y = number of food processors are sold

Profit function z = 2000x + 3000y

Objective function
Maximize Z = 2000x + 3000y

Constraints are 
3x + 3y ≤ 36        (above machine A)
5x 2y ≤ 50           ( about machine B)
2x + 6y ≤ 60        ( about machine C)

As the number of mixers and food processors are non-negative.

x ≥ 0, y ≥ 0
Mathematical model of L.P.P. is
Maximize Z = 2000x + 3000y

Subject to 
3x + 3y ≤ 36 
5x 2y ≤ 50     
2x + 6y ≤ 60
and x ≥ 0, y ≥ 0