Implement the following LP problem in a spreadsheet. Use Solver to solve the problem and create a Sensitivity Report. Use this information to answer the following questions:

MAX: $4$X$1+4$X$2$

Subject to: $2$X$1+4$X$2<=20$

$3$X$1+5$X$2<=15$

X$1,$ X$2>=0$

$($a$)$

What range of values can the objective function coefficient for variable X$1$ assume without changing the optimal solution? $($If there is no limit on how much the coefficient can increase or decrease, enter $\backslash$infty $.)$

The objective function coefficient for variable X$1$ can decrease by

Incorrect: Your answer is incorrect.

or increase by

Incorrect: Your answer is incorrect.

without changing the optimal solution.

$($b$)$

Is the optimal solution to this problem unique, or are there alternate optimal solutions?

None of the allowable increase or decrease values for the objective coefficients are zero, so the optimal solution is unique.

We cannot determine if the optimal solution is unique based on our sensitivity report because the solution is degenerate.

Some of the allowable increase or decrease values for the RHS values are zero, so there are alternate optimal solutions.

None of the allowable increase or decrease values for the RHS values are zero, so the optimal solution is unique.

Some of the allowable increase or decrease values for the objective coefficients are zero, so there are alternate optimal solutions.

Incorrect: Your answer is incorrect.

$($c$)$

How much does the objective function coefficient for variable X$2$ have to increase before it enters the optimal solution at a strictly positive level? $($Round your answer to three decimal places.$)$

$2\mathrm{.}345$

Incorrect: Your answer is incorrect.

$($d$)$

What is the optimal objective function value if X$2$ equals $1?($Round your answer to three decimal places.$)$

$($e$)$

What is the optimal objective function value if the RHS value for the second constraint changes from $15$ to $20?($Round your answer to three decimal places.$)$

$33\mathrm{.}33$

$()$

Is the current solution still optimal if the coefficient for X$2$ in the second constraint changes from $5$ to $1?$ Explain. $($Round your answer to three decimal places.$)$

If we change this coefficient from $5$ to $1,$ then the new reduced cost for X$2$ for our current solution would be

$.$ Therefore, it

$---$Select$---$

be profitable to increase the value of X$2$ and the current solution would

$---$Select$---$

be optimal

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