Given this LP model:
minimize Z = 4x1 + 8x2
subject to
Fiber 5x1 + 8x2 ≥ 40
Protein 6x1 + 4x2 ≥ 24
x1, x2 ≥ 0
a. Find the range of optimality or insignificance for each objective function coefficient.
b. How would a decrease of $1 in the x1 coefficient of the objective function affect the optimal values of the decision variables? How would it affect the optimal value of the objective function?
c. What is the shadow price for the fiber constraint's RHS? Over what range of values is it valid?
d. What is the shadow price for the RHS of the protein constraint? Over what range of values is it valid?
e. What impact on cost would a decrease of 2 units in the RHS of the protein constraint have?