Problem $3.$ A truck maintenance shop is considering two locations. In location $1$ they expect a demand of

$15$ trucks per day and in location $2$ they expect a demand of $20$ trucks per day. The service time per truck is

$1$ hour and they operate $8$ hours per day. Each location can have at most $5$ repair bays. Location $1$ has a

monthly lease cost of $$20$K while for location $2$ is $$28$K$.$ The monthly costs associated with each bay is $$9$K

$($labor and equipment maintenance$/$ rent$).$ The revenue per truck is $$350.$ Assume $250$ days per year.

Complete all calculations on an annual basis. Waiting costs are $$180/$hour$.$

$-$ Determine the profit per location$/$configuration and make a recommendation.

$-$ Develop a sensitivity plot based on the waiting cost $($x variable$),$ ranging from $$100/$hour to

$$250/$hour$.$ Explain the graph results. Note the best number of repair bays per location may change

as z changes.

I will apreaciate a step by step answer.