Consider the problem Find the minimum solution to this problem. If required, rou

Question

Consider the problem

Find the minimum solution to this problem. If required, round your answers to two decimal places.

Optimal solution is X = ______ , Y =______ , for an optimal solution value of______ .

If the right-hand side of the constraint is increased from 8 to 9, how much do you expect the objective function to change? If required, round your answer to two decimal places.

Decrease by ______.

Resolve the problem with a new right-hand side of 9. How does the actual change compare with your estimate? If required, round your answers to two decimal places.

Objective function value is ____ so the actual decrease is only_____ rather than ____

Min   2X2 – 18X + 2XY + Y2 – 16Y + 49 s.t. X + 4Y 8

Explanation / Answer

Solving the given problem in excel solver we get:

If we see the sensitivity report:

the Shadow price of the constraint RHS is -1.68 (rounded off)

hence, if we increase the RHS from 8 to 9, the objective function value will decrease by 1.68.

Solving with RHS =9:

the Objective Function value is 0, so actually the decrease is only 1.64 rather than 1.68.

Min   2X2 – 18X + 2XY + Y2 – 16Y + 49 s.t. X + 4Y 8 X Y 3.52 1.12 LHS Sign RHS s.t. 8 <= 8 O.F. 1.64

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