Scenario $8\mathrm{.}2-$ Willow

A company faces the aggregate planning problem shown in the table below. Cost of regular production is $$8$ per unit, the cost of producing the same unit on overtime is $$15,$ the cost of subcontracting is $$12$ per unit, and the cost of carrying a unit in inventory from one month to the next is $$6.$

$\backslash$table$[[,$January,February,March,April,May$],[$Forecast$,400,800,1200,700,300],[$Beginning Inventory,$100,,,,],[$Regular Time,,,,,$],[$Overtime$,,,,,],[$Subcontracting$,,,,,],[$Ending Inventory,,,,,$]]$

The labor contract at the plant prohibits both overtime and subcontracting output to exceed $400$ units in any five$-$month window. The plant capacity is $20$ units per day produced using two shifts and the plant runs seven days a week. By policy, management wants to avoid stockouts.

Without actually solving the aggregate planning problem, it is safe to conclude that in the optimal solution to Scenario $8\mathrm{.}2,$

Select one:

a$.$ the number of units made using regular time will exceed the forecast.

b$.$ the number of units made using subcontracting will exceed the number of units made using regular time.

c$.$ the total ending inventory will exceed the number of units made using overtime.

d$.$ the number of units made using subcontracting will exceed the number of units made using overtime.