Problem $3(40\%)$: Chapter $3-$ Question $3,$ Parts a and b$.$ Note, an "extreme point" is the intersection

of two constraints and are the corner points for the feasible region shape. Do not replicate the graph

in this problem in your Excel worksheet. Just answer the following questions.

Complete Parts a and b as written in the textbook. Then, complete the questions below.

c$.$ optimal value to change, what are the new optimal solution and optimal value? What is

the objective function value for the objective function line through the point $(1,1)?$

$($Another name for the objective function line is "isoprofit line," see page $24$ in the

textbook for a description.$)$

d$.$ What is the objective function value for the objective function line through the point $(3,3)?$

Is this an improvement to the answer in part c $?$

e$.$ Which best describes the linear program $($LP$)$: infeasible, unique optimal solution,

alternate optimal solution, or unbounded optimal solution? Why?

f$.$ For this part only, consider the following additional constraint:

"Organic Greenhouses signed a contract with a local grocery chain to provide at least $6$

acres of tomatoes."

Answer the following questions:

Will the original feasible region stay the same, increase, or decrease?

Will the optimal value stay the same, increase, or decrease?

If the constraint change does cause the optimal solution and