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

a) Determine the optimal solution using LP software.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 firm’s profit increase if an extra 10 hours of time were made available on the second machine at no extra cost?

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Maximize contribution = 4X₁ + 4X2 + 7X3 Subject to: 1X₁ +7X₂ + 4X3 ≤ 100 (hours on machine 1) 2X₁ + 1X₂ +7X3 ≤ 110 (hours on machine 2) 8X₁ + 4X₂ + 1X3 ≤ 100 (hours on machine 3)