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

Question

Consider the problem

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.

?

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 icrease/decrease? is only ? rather than ?

(please fill in all question marks)

Min   2X2 – 22X + 2XY + Y2 – 12Y + 65 s.t. X + 4Y 8

Explanation / Answer

put x=0 then y=2 ie (0,2)

put y=0 then x=8 ie ( 8,0)

let f(x,y) =2X2 – 22X + 2XY + Y2 – 12Y + 65

f(0,2)=0-0-0+4-24+65=45;

f(8,0)=128-192-0-0-0+65=1

ie the min value is 1 at x=8,y=0

b)

Min   2X2 – 22X + 2XY + Y2 – 12Y + 65 s.t. X + 4Y 8

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