Consider a manufacturing facility that produces five different products using four machines. The facility has four machines of type $1,$ five of type $2,$ three of type $3$ and seven of type $4.$ Each machine operates $40$ hours per week. The problem is to determine the optimum weekly production quantities for the products. The goal is to maximize total profit. Analyze the sensitivity report.

Machine Quantity Product $1$ Product $2$ Product $3$ Product $4$ Product $5$

M$141\mathrm{.}21\mathrm{.}30\mathrm{.}700\mathrm{.}5$

M$250\mathrm{.}72\mathrm{.}21\mathrm{.}60\mathrm{.}51$

M$330\mathrm{.}90\mathrm{.}71\mathrm{.}310\mathrm{.}8$

M$471\mathrm{.}42\mathrm{.}80\mathrm{.}51\mathrm{.}20\mathrm{.}6$

Unit profit, $ $1825101215$