$3.$ Sensitivity Analysis: Complete the following probleus on $($Good$-$to$-$Go Suitcase Company$)$ in Chapter $4$ from your textbook. $($Note: All information you need to answer the questions are given in the tables shown. If necessary, use separate sheet of paper for work$).$ All analysis must be done on paper. No credit if Excel is used. For full credit, show all work and calculations on paper to support your answers, and respond with complete statements where needed.

$($a$)$ Complete Problem $4-22,$ Page $228,$ all parts.

$($b$)$ The optimal solution to Luxury models is $0$ units. Explain why. Further tell what kind of impact the company may experience if the company forces itself to make at least one Luxury model.

$($c$)$ The company has an opportunity to get $175$ additional hours finishing time, but at a cost of $\backslash (\backslash$$ $14\backslash )$ per hour rather than the current $\backslash (\backslash$$ $9\backslash ).$ Is it profitable for the company to get these additional hours? Will the current optimal solution change? If possible, determine the change in the total profit.

$($d$)$ Determine the range of optimality for the unit labor cost of Luxury model.

$($e$)$ The unit selling price of Standard model will increase by $\backslash (\backslash$$ $2\mathrm{.}85\backslash ),$ and the unit selling price of Deluxe model decreases by $\backslash (\backslash$$ $1\mathrm{.}50\backslash ).$ What is the impact of these changes on the optimal solution and the profit made?

$($f$)$ The company management is planning to reduce Cutting $\backslash$& Coloring time by $15$ hours, increase Finishing time by $50$ hours, decrease Quality $\backslash$& Packaging time by $25$ hours, and increase unit selling price of Deluxe models by $\backslash (\backslash$$ $2\backslash ),$ while keeping all other parameters the same. Assess the impact of these changes on the total profit.

$($g$)$ Complete Problem $4-23,$ Page $229.$