A factory produces two compounds P and Q. The following table gives the units of ingredients A and B (per unit) of compounds P and Q and also minimum requirement of P and Q. Cost per unit of P and Q are also given:

 

Compound per unit

Minimum

Ingredient

P

Q

Requirement

C (per unit)
D (per unit)

1
3

2
1

80
75

Cost per unit (in Rs)

4

6

 

Find the quantities of P and Q which would minimize the cost.

Asked by Topperlearning User | 4th Jun, 2014, 01:23: PM

Expert Answer:

Let x units of P and y units of Q be produced we have the following LPP
          Minimise z = 4x + 6y
          st x + 2y  80
          3x + y  75
          x  0, y 0
         

Corner Points

Z = 4x + 6y

A(80, 0)
B(14, 33)
C(0, 75)

z = 320
z = 254
z = 450

Z is minimum at B(14, 33)
Hence, the cost is minimum when 14 units of P and 33 units of Q are produced and minimum cost is Rs 254.

Answered by  | 4th Jun, 2014, 03:23: PM