Consider the problem Min 2X^2 - 18X + 2XY + Y^2 - 16Y + 52 s.t. X + 4Y lessthano

Question

Consider the problem Min 2X^2 - 18X + 2XY + Y^2 - 16Y + 52 s.t. X + 4Y lessthanorequalto 8 a. 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 b. 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. by c. 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 is only rather than

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 -1.67999 (rounded off)

hence, if we increase the RHS from 8 to 9, the objective function value will decrease by 1.67999.

Solving with RHS =9:

the Objective Function value is 3, so actually, the decrease is only 1.64 rather than 1.67999.

DO THUMBS UP ^_^

Min   2X2 – 18X + 2XY + Y2 – 16Y + 52 s.t. X + 4Y 8 X Y 3.52 1.12 LHS Sign RHS s.t. 8 <= 8 O.F. 4.64

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