$2.(30$ points$)$ Refer to Question $2$ of Homework Assignment $1($repeated below$).$

The Electrotech Corporation manufactures two industrial$-$sized electrical devices: generators and alternators. Both products require wiring and testing during the assembly process. Each generator requires $2$ hours of wiring and $1$ hour of testing and can be sold for a $\backslash (\backslash$$ $250\backslash )$ profit. Each alternator requires $3$ hours of wiring and $2$ hours of testing and can be sold for a $\backslash (\backslash$$ $150\backslash )$ profit. There are $260$ hours of wiring time and $140$ hours of testing time available in the next production period and Electrotech wants to maximize profit.

a$.$ Solve the problem using Solver in Excel and generate the Answer and Sensitivity Reports $(5$ points$)$

b$.$ How much excess wiring and testing capacity exists in the optimal solution? $(5$ Points$)$

c$.$ What is the company's total profit if it has $10$ additional hours of wiring capacity? $(10$ Points$)($No points will be given if you just re$-$solve the problem. Use the sensitivity report.$)$

d$.$ By how much does the profit on alternators need to increase before their production is justified? $(10$ Points$)$