Consider the following LP problem developed at Zafar Malik\'s Carbondale, Illino

Question

Consider the following LP problem developed at Zafar Malik's Carbondale, Illinois, optical scanning firm Maximize Z= 1x1+1x2 (C1) 360 (C) Subject to:2x,+1X,s60 1x,+ 2X, On the graph on right, constraints C, and C, have been plotted a) Lizing the poin drawing tool, plot all he comer points for the feasible area The optimum solution is: Xi= (round your response to two decimal places) X2= (round your response to two decimal places, Optimal solution value Z = round, our response to no decimal places, d your response to two decimal places)

Explanation / Answer

Solve (C1) and (C2),

The intersection point = B = (20,20)

Corner points            Z = x1 + x2

A= (0,30)                 Z = 0 + 30 = 30

B= (20,20)               Z = 20 + 20 = 40
C= (30,0)                 Z = 30 + 0 = 30

The Maximum value of Z = 40, the corresponding point is Optimum point B = (20,20)

a) The optimum solution is

X1 = 20

X2 = 20

The Optiomum solution of Z = 40

b) If raised the profit $3 of X1

Corner points            Z = 3x1 + x2

A= (0,30)                 Z = 3(0) + 30 = 30

B= (20,20)               Z = 3(20) + 20 =80
C= (30,0)                 Z = 3(30) + 0 = 90

The optimum solution (Point C) is

X1 = 30

X2 = 0

The Optiomum solution of Z = 90

c)

If raised the profit $1.25 of X1

Corner points            Z = 1.25x1 + x2

A= (0,30)                 Z = 1.25(0) + 30 = 30

B= (20,20)               Z = 1.25(20) + 20 = 45
C= (30,0)                 Z = 1.25(30) + 0 = 45

The optimum solution (Point B and C) is

X1 = 30

X2 = 0

and X1 = 20, X2 = 20

The Optiomum solution of Z = 45

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