Q$1.$ Prestige, Inc. needs an aggregate plan for its product line. As part of trying to maintain a lean production system, management prefers a constant workforce, no overtime, and constant production level while also minimizing safety stock. Relevant data follows:

$\backslash$table$[[$Item$,$Data,Units$],[\backslash$table$[[$Productio$],[$n time$],[$required$]],4\mathrm{.}5,\backslash$table$[[$labor$],[$hours per$],[$unit$]]],[\backslash$table$[[$Straight$],[$timelabor$],[$cost$]],$$$24,$Font$],[$Workday$,7\mathrm{.}5,\backslash$table$[[$hours per$],[$day$]]],[\backslash$table$[[$Beginning$],[$inventory$]],250,$units$]]$

$\backslash$table$[[$Item$,$Data,Units$],[\backslash$table$[[$Safety$],[$stock$],[$target$]],10\%,\backslash$table$[[\%$ of$],[$monthly$],[$forecast$]]],[\backslash$table$[[$Shortage$],[$cost$]],$$$75,$per unit$],[\backslash$table$[[$Inventory$],[$holding$],[$cost$]],$$$10,\backslash$table$[[$per unit$],[$per month$]]],[\backslash$table$[[$Overtime$],[$labor cost$]],$$$5,$per hour$]]$

$\backslash$table$[[$Item$,$Data,Units$],[\backslash$table$[[$Hiring$],[$cost$]],$$$10,000,$per person$],[\backslash$table$[[$Laying off$],[$charge$]],$$$20,000,$per person$],[\backslash$table$[[$Number of$],[$workers$]],72,$people$]]$

The sales forecast for next year is:

$\backslash$table$[[$Month$,$Forecast,$\backslash$table$[[$Working$],[$Days$]],$Month,Forecast,$\backslash$table$[[$Working$],[$Days$]]],[$Jan$,2000,20,$Jul,$4000,21],[$Feb$,1500,18,$Aug,$4500,23],[$Mar$,2000,22,$Sep,$4000,20],[$Apr$,2500,20,$Oct,$3000,24],[$May$,3000,22,$Nov,$2500,19],[$Jun$,3500,21,$Dec,$1500,15]]$

Other assumptions:

Inventory holding costs are not charged for safety stock.

Safety stock is never produced using overtime.

Even though the production time is $7\mathrm{.}5$ hours per day, workers are paid for $8$ hours per day.

Worker hires or layoffs take effect on the first day of the plan month.

Backorders are carried over month$-$to$-$month

part A What is the total cost for this plan? $($HINT: Use a level strategy$)$

part B Instead of enduring the increased shortage costs, management decides to use OT to make up any shortfalls. What is the cost of this plan and how does it compare to part A$?($HINT: Use a hybrid strategy$)$