Minimize (costs) Z = 4X1 + 8X2

Subject to Fiber 5X1 + 8X2 > 40
Protein 6X1 + 4X2 > 24
X1, X2 > 0

a.) What is the optimal value of the objective function?
b.) What are the optimal values of the two decision variables?
c.) Find the range of optimality for each objective function coefficient.
d.) How would a decrease of $1 in the X1 coefficient of the objective function affect the optimal values of the decision variables?
e.) How would a decrease of $1 in the X1 coefficient of the objective function affect the optimal value of the objective function?
f.) What is the dual value (AKA “shadow price) for the RHS of the protein constraint?
g.) What is the range of feasibility of the dual value for the RHS of the protein constraint?
h.) What impact on total cost would a decrease of 2 units in the RHS of the protein constraint have? Please explain the rationale for your answer