maximize profit: $42$x

Consider the linear optimization model displayed above.

$1.$ Set$-$up the model in an Excel spreadsheet.

$2.$ Use the Solver add$-$in to solve for the optimal solution.

$3.$ Generate the answer and sensitivity reports from Solver.

After solving the problem and generating the Solver reports, answer the following questions:

a$)$ What is the optimal value of X$?$

b$)$ What is the optimal value of Y$?$

c$)$ What is the optimal value of Z$?$

d$)$ What is the value of the objective function at the optimal solution?

e$)$ Suppose the right$-$hand side $($RHS$)$ of the first constraint were increased by $5.$ How much will the objective function increase?

f$)$ How many of the constraints are binding?

g$)$ How much can the coefficient of Y in the objective function increase before the optimal product mix changes?

h$)$ One of the decision variables takes the value of $0$ at the optimal solution. What objective function coefficient value would cause the optimal solution to have a non$-$zero value for this decision variable?