1.Solve the following LP Problem

Max Z=8X1+10X2

S.T. X1+4X2<=12

3X1+2X2<=12

2X1+X2 <=8

X1,X2>=0

2.Solve the following LP Problem

Max Z=3X1+5X2

S.T. 4X1+3X2>=24

2X1+3X2<=18

X1,X2>=0

3.Solve the following LP Problem

Max Z=5X1+7X2

S.T. X1<=6

2X1+3X2<=19

X1+X2 <=8

X1,X2>=0

For Each:

a) Solve the Problem.

b) Identify the reduced costs and Interpret each

c) Calculate the range of optimality for each objective function coefficient.

d) Identify the slacks for the resources and calculate the shadow price for each resource