Take$-$Home Individual Midterm Project $($Case $2).(100$ p$.)$

XYZ Ltd produces two popular grades of commercial carpeting among its many other products. In the coming production period, XYZ needs to decide how many rolls of each grade should be produced in order to maximize total profit. Each roll of Grade X carpet uses $50$ units of synthetic fiber, requires $10$ hours of production time, and needs $20$ units of foam backing. Each roll of Grade Y carpet uses $40$ units of synthetic fiber, requires $28$ hours of production time, and needs $15$ units of foam backing.

The profit per roll of Grade X carpet is $$200$ and the profit per roll of Grade Y carpet is $$160.$ In the coming production period, XYZ has $3000$ units of synthetic fiber available for use. Workers have been scheduled to provide at least $1800$ hours of production time $($overtime is a possibility$).$ The company has $1500$ units of foam backing available for use. XYZ wants to develop and solve a linear programming model for this problem.

Note: Provide your answers in the space indicated below.

a$.(10$ p$.)$ Define the decision variables.

b$.(10$ p$.)$ Define the objective function.

c$.(10$ p$.)$ Define the constraints.

d$.(70$ p$.)$ Solve the LP using Excel$$s solver.

i$.(20$ p$.)$ The solution to the LP is: $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

Fully interpret your answer in p$.($i$)$ above.

ii$.(10$ p$.)$ The value of the objective function is: $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

Fully interpret your answer in p$.($ii$)$ above.

iii. $(10$ p$.)$ The binding constraint$($s$)$ is $($are$)$: $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

Fully interpret your answer in p$.($iii$)$ above.

iv$.(10$ p$.)$ The nonbinding constraint$($s$)$ is $($are$)$: $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

Fully interpret your answer in p$.($iv$)$ above.

v$.(20$ p$.)$ Include two relevant Excel$$s solver printouts $($Sheet and Answer Report$)$ as exhibits at the end of your report.

Note: On the Title Page, please provide only your full name $($Last and First$).$

Note: Save everything above as one and only one file in the pdf format and email to me as an attachment $($no cloud sharing$).$ Additional instructions are provided in the Course Syllabus $$ please follow them.

Note: Do not attach in your email any additional Excel files $$ they will not be marked.