Problem $12$

$\backslash$table$[[$Month$,$Forecasted Demand,$],[,],[$July$,1,250,],[$August$,1,100,$W$],[$September$,950,$th$],[$October$,900,$f$],[$November$,1,000,],[$December$,1,150,]]$

The personnel department of the A&M Corporation wants to know how many workers will be needed each month for the next six$-$month production period. The following is a monthly demand forecast for the six$-$month period.

The inventory on hand at the end of June was $500$ units. Each unit requires five employee$-$hours to produce, there are $20$ working days each month, and each employee works an eighthour day. The workforce at the end of June was $35$ workers. It costs $$500$ for each worker hired. Severance pay amounts to $$1000$ per worker. Each employee get paid $$8\mathrm{.}00$ per hour. It costs $$10$ per month to hold each unit of inventory. Overtime is NOT allowed. HINT: Determine $K$ in terms of units per day per worker

a$)$ Determine a minimum inventory production plan $($i$.$e$.,$ one that allows arbitrary hiring and firing$).$

b$)$ Determine the production plan that meets demand but does not hire or fire workers during the six$-$month period.

c$)$ Let's say subcontracting is allowed. Let's say we implement the constant workforce with subcontracting plan, what would the cost of subcontracting need to be to beat the cheaper of the two options above?

d$)$ Using this subcontracting cost of $$50,$ formulate a LP and solve to optimality for the constraints of this problem

I highly recommend solving parts $A,B,$ and C by hand and checking against the excel worksheet.