Question

Kalyan Singhal Corp. makes three products, and it has three machines available as resources as given in the following LP problem:Maximize contribution = 6X1 + 8X2 + 4X3Subject to:1X1 + 7X2 + 4X3 <= 72(hours on machine 1)2X1 + 1X2 + 7X3 <= 76 (hours on machine 2)8X1 + 4X2 + 1X3 <= 72 (hours on machine 3)X1, X2, X3 >=0(a) Determine the optimal solution using LP software. the optimal achieved isX1=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 firm’s profit increase if an extra 15 hours of time were made available on the second machine at no extra cost?

Answer 1

Answer:

a) X1=5.64

X2=4.57

X3= 8.59

Optimal solution=104.77

b) Additional hour on machine 3 = 105.42 – 104.77 = 0.64

c) Additional 15 hours on machine 2 = 105.37-104.77 = 0.6

Explanation:

Please consider the data provided by the exercise. If you have any question please write me back. All the exercises are solved in a single sheet with the formulas indications.  SOLVED WITH EXCEL SOLVER.

Answer 2

The optimal solution shows the value of X1, X2, and X3 to be 5.64, 4.57, and 8.59 respectively.

How to determine the optimal solution

It should be noted that an optimal solution simply means a feasible solution where the objective function has reached either the maximum or minimum value.

In the table attached, the optimal solution shows the value of X1, X2, and X3 to be 5.64, 4.57, and 8.59 respectively.

Furthermore, the additional hour from machine 3 will be;

= 105.42 - 104.77

= 0.64

Lastly, the additional 15 hours on machine 2 will be:

= 105.37 - 104.77

= 0.6

The information is depicted in the table attached.

Learn more about optimal solution on:

https://brainly.com/question/15356519