Question

Problem 8-02 (Algorithmic) Consider the problem Min 2x2 18X2XY - 18Y58 X 4Y 8 s.t. a. Find the minimum solution to this problem. If required, round your answers to two decimal places. for an optimal solution value of Optimal solution is X Y 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 How does the actual change compare with your estimate? If required, round your answers to two decimal places. Objective function value is is only rather than so the actual

Answer 1

f(x) 2x-18 2xy -18y 58 fr 4x 1 A fy 2r2y- 18 4 this gives the critical points -3A fy f 3A-2x >x 2 7A y 9

min. of

18.x2yy 18y 58 -3A 18( -3A 7A 9) 2 -3A 7X 7A 2( 2 9) 18( 9)58 2 -) 2( 2 2 2 4.5A227A 10.5A2 27A +12.25 81 +63A 63A 162 58 27.25A2 23 7A 4 2 subjected to x +4y 8> A-2.24 +9) 8-> 12.5A-28 2

27.25A2 入 - 23 27.25(-2.24)2- 23 136.7296 23 113.7296

=2.24 A 32.24/2 3.36 y 7* -2.24/2 +9 9- 7.84 1.16

i have used lagrange multplier method

in which i first took derivative of objective function with respect to x and equated it with derivative of subjected function multiplied by lambda.