Based on the Variable Cells

Constraintsoptimal results and the sensitivity report, answer the following independent questions:

$($b$)$ What is the least expensive redistribution plan for the vehicles? Which location still has excess vehicle$($s$)$ and how many? $(7$ marks$)$

$($c$)$ Is there any alternative redistribution plan with the same total cost? Explain. $(2$ marks$)$

$($d$)$ The route from location $1$ to location $5$ usually has less traffic. Holding all other factors remain unchanged, how much does the movement cost $($per vehicle$)$ on this route need to be changed for it to be worthy for use? $(2$ marks$)$

$($e$)$ Suppose a vehicle at location $4$ needs to go for repair and maintenance, how would the minimum total cost in part $($b$)$ be affected? $(2$ marks$)$

$($f$)$ The logistics company could consider an option of renting a vehicle to fulfill the requirement at location $1,2$ or $6$ if it could achieve cost saving. To save as much cost as possible, which of these locations should be offered a rented vehicle, and up to what rental cost should the company consider this option? Explain. $(5$ marks$)$

$($g$)$ Suppose the fuel cost will increase simultaneously by the same percentage, denoted by p$,$ on every route. For example, if p $=10\%,$ the cost to move a vehicle from location $4$ to location $1$ will increase by $$2\mathrm{.}50(=$ $$25*10\%).$ What is the maximum value of p$,$ denoted by pmax, so that the redistribution plan in part $($b$)$ remains unchanged? Accordingly, determine the new total cost in terms of pmax.