Kalyan Singhal Corp. makes three products, and it has three machines available as resources as given in the following LP

problem:

Maximize contribution=

4x₁ +4x₂ + 7x₃

1x₁ + 7x₂ + 4x₃ <=100 C1: hours on machine 1

2x₁ + 1x₂ + 7x₃ <= 110 C2: hours on machine 2

8x₁ + 4x₂ + 1x₃ <=100 C3: hours on machine 3

x₁,x₂,x₃ >=0

a) Using a computer software for solving LP, the optimal solution achieved is

X1=

X2-

X3=

contribution =

(b) Is there unused time available on any of the machines with the optimal solution?

(c) What would it be worth to the firm to make an additional hour of time available on the third machine?

(d) How much would the firms profit increase if an extra 15 hours of time were made available on the second machine at no extra cost?