Consider the Linear Program MAXIMIZE Z 5X 1 8X 2 Subject to X 1 2X 2 62 2 X 1 2X 2 224 X 1 and X 2 0 a Sketch the Region of Feasible solutions and list all corner point of the region of feasible solution b Calculate the number of units of slack in constraint1 X 1 2X 2 224 d specify the two binding constraints for this problem at the optimal solution e calculate ( derive by hand) the shadow price for an additional unit added to the RHS of constraint2 2 X 1 2X 2 100 ( keep 3 decimal place in your calculations)

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Question: Consider the Linear Program: MAXIMIZE Z = 5X 1 + 8X 2 Subject to: X 1 + 2X 2 < = 62 2 X 1

Consider the Linear Program: MAXIMIZE Z = 5X₁ + 8X₂

Subject to: X₁ + 2X₂ < = 62

2 X₁ + 2X₂ <= 100

4X₁ + 7X₂ >= 224

X₁ and X₂ >= 0

a. Sketch the Region of Feasible solutions and list all corner point of the region of feasible solution

b.Calculate the number of units of slack in constraint1: X₁ + 2X₂ <= 62

c. calculate the number of units of surplus in constraints3: 4X₁ + 7X₂ >= 224

d. specify the two binding constraints for this problem at the optimal solution

e. calculate ( derive by hand) the shadow price for an additional unit added to the RHS of constraint2: 2 X₁ + 2X₂ 100 ( keep 3 decimal place in your calculations)

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