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$\backslash$table$[[$Cell$,$Name,Final Value,Shadow Price,$\backslash$table$[[$Constraint R$.$H$.],[$Side$]],\backslash$table$[[$Allowable$],[$Increase$]],$Allowable Decrease$],[$$ G$$8,$Drilling Hours,$700\mathrm{.}0,22\mathrm{.}4,700,3\mathrm{.}36,298\mathrm{.}33],[$$$G$$$9,$Milling Hours,$886\mathrm{.}8,0\mathrm{.}0,890,1E+30,3\mathrm{.}21],[$$G$$10,$Lathe Hours,$1205\mathrm{.}0,5\mathrm{.}9,1205,17\mathrm{.}58,427\mathrm{.}22],[$$ G$$$11,$Inspection Hours,$404\mathrm{.}6,0\mathrm{.}0,525,1E+30,120\mathrm{.}40]]$

This sensitivity report above shows the result of a linear program to find the optimal product mix between four possible products $($Gears A$,$ B$,$ C$,$ and D$)$; to make these $4$ gears, you need to use the following resources: drilling hours, milting hours, lathe hours, and inspection hours. The coefficients of the objective function represent the profit to be made from the manufacture of each type of gear.

Answer each of the following questions and be as specific as possible. Wherever it is possible to compute a profit or the production plan, please do so and show your workt

a$.$ What is the impact on the profit and production plan if the number of drilling hours is increased to $703?$

b$.$ What is the impact on the profit and production plan if the number of milling hours is decreased by $3$ hours?

c$.$ What is the impact on the profit and production plan if the number of lathe hours is decreased to $800?$

d$.$ What is the impact on the profit and production plan if the number of inspection hours is increased by $25$ hours?

e$.$ How do binding constraints differ from non$-$binding constraints?

f$.$ What is the impact on the profit and production plan if the number of lathe hours is increased to $1235$ hours?

d States$)$

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