Consider the following linear program: Max 5x1 + 9x2 s.t. 1/2x1 + 1x2 < 8 1x1 +

Question

Consider the following linear program:

Max 5x1 + 9x2

s.t.

1/2x1 + 1x2 < 8

1x1 + 1x2 > 10

1/4x1 + 3/2x2 > 6

X1, x2 > 0

a)     Write the problem in a standard form.

b)     Solve the LP problem using graphical method. Make sure to show the feasible region and all the extreme or corner point solutions. Identify the solutions in the feasible region.

c)     Find the optimal solution and the slack or surplus variables.

Consider the following linear program: Max 5x1 + 9x2 s.t. 1/2x1 + 1x2 10 1/4x1 + 3/2x2 > 6 X1, x2 > 0 Write the problem in a standard form. Solve the LP problem using graphical method. Make sure to show the feasible region and all the extreme or corner point solutions. Identify the solutions in the feasible region. Find the optimal solution and the slack or surplus variables.

Explanation / Answer

STANDARD FORM

Z= 5X1+ 9 X2+0S1+0S2+0S3

0.5X1+X2+S1=8

X1+X2-S2=10

0.25X1+1.3X2-S3 =6

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