A furniture manufacturer produces two types of tables $($country and contemporary$)$ using three types of machines. The minutes required to produce the tables on each machine is given in the following table. Country tables sell for $$350$ and contemporary tables sell for $$450.$ Management has determined that at least $20\%$ of the tables made should be country and at least $30\%$ should be contemporary. We want to maximize its revenue. The excel sheet is on Canvas named: Prob$3\_13\_2$ Use Solver to create a Sensitivity Report and answer the following questions: a$.$ If the company could get $50$ more units of routing capacity, should they do it$?$ If so$,$ how much should they be willing to pay for it$?$ b$.$ If the company could get $50$ more units of sanding capacity, should they do it$?$ If so$,$ how much should they be willing to pay for it$?$ c$.$ Suppose the polishing time on country tables could be reduced from $2\mathrm{.}5$ to $2$ units per table. How much should the company be willing to pay to achieve this improvement in efficiency? d$.$ Contemporary tables sell for $$450.$ By how much would the selling price have to decrease before we would no longer be willing to produce contemporary tables? Does this make sense? Explain. e$.$ Create a Spider Plot showing the effect on optimal profit of varying the availability of each resource between $90\%$ and $110\%$ of its base case value in $2\%$ increments. Describe the information illustrated by this plot.

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