Exercise $1.$ Develop an Excel LP model of the following problem and solve it$.$ Dan and Joel own a retro game shop, and one of the things they offer is old gaming consoles $($specifically$,$ the Nintendo Entertainment System $($NES$)$ and the Gamecube$).$

To repair an NES, it requires $3$ hrs$.$ of labor and $4$ spare parts, while repairing a Gamecube requires $5$ hrs$.$ of labor and $2$ spare parts. In the workbook, enter these numbers under the constraint section.

Unfortunately, these systems are a little old, so they can only buy so many per week. More specifically, they can buy a maximum of $10$ NES and $20$ Gamecubes per week to repair. Because they also run the store, they only have $50$ hours per week to devote to repairing. Finally, due to a shortage of parts, they can only buy $60$ spare parts at a time. Enter these numbers under the Quantity Available column.

They can sell the NES for $$50$ and the Gamecube for $$75.$ Enter these numbers next to Profit per Console cell.

a$)(4$ points$)$ Using Solver, calculate the optimal profit level. Remember that Total Profit depends on the number of Consoles Repaired and Profit per Console.

Use the SUMPRODUCT formula function to calculate the profit function value and total resource usage as appropriate. The SUMPRODUCT function allows you to calculate the sum of the product of arrays of the same dimension.

To solve the model, use the Solver under the Data tab. You may need to add Solver as an Add In$.$ See the lecture slides on Linear Programming for an overview. Specify the constraints as mentioned in the slides.

Since the number of Consoles Repaired has to be an integer, make sure you add two constraints for cells C$4$ and D$4$ to be integer.