Homework $7$ Sensitivity Analysis

Consider the following problem.

Maximize $50$x$1+60$x$2+55$x$3$

Subject to:

x$1+$ x$2+$ x$3<=100$

$2$x$1+3$x$2+2$x$3<=300$

$2$x$1+3$x$2+2$x$3>=250$

x$1+2$x$3>=60$

x$1,$ x$2,$ x$3>=0$

a$.$ Use solver to get the sensitivity report and copy the report. Then use the report to answer the following questions.

b$.$ State the optimal solution.

c$.$ What is the optimal objective function value?

d$.$ What would happen to the optimal solution if

a$.$ The unit profit on x$2$ decreases by $20?$

b$.$ The unit profit on x$3$ decreases to $45?$

c$.$ The unit profit on x$1$ and x$3$ change to $53?$

e$.$ Interpret the reduced cost for x$1.$

f$.$ What would happen to the objective function if

a$.$ The RHS of constraint $1$ increases by $5?$

b$.$ The RHS of constraint $2$ decreases to $250?$

c$.$ The RHS of constraint $4$ change to $44?$

g$.$ Which constraints are binding?

h$.$ What are the slack$/$surplus values?