Problem $1.$ Given the input data to S&OP plan, answer the following questions:

Beginning Ending Backorder

Sales in Production in Inventory Inventory

Month Sales Labor hour Working labor$-$hour Number of Workers Workers Labor$-$hour Labor$-$hour Labor$-$hour

$($Million$)(000$s$)$ days $(000$s$)$ Workers Hired Fired $(000$s$)(000$s$)(000$s$)$

$1900113\mathrm{.}30$

January $820$

February $7\mathrm{.}421$

March $11\mathrm{.}223$

April $1220$

May $9\mathrm{.}822$

June $8\mathrm{.}522$

July $920$

August $11\mathrm{.}623$

September $9\mathrm{.}420$

Use the following data for your spreadsheet:

Unit cost $$10$

Sales per direct labor hour $$30$

Hiring cost $ $300\mathrm{.}0$

Firing cost $ $500\mathrm{.}0$

Production cost per labor hour $ $15\mathrm{.}00$

Backorder cost per labor hour per month $$2$

Inventory carrying cost per labor hour per month $$0\mathrm{.}1$

Number of Employees as of end of last December $1900$

Employee Working Hours $($in hours$/$day$)8$

Based on level strategy $($i$.$e$.$ you have a constant number of workers from January to September$)$

$($a$)$ Convert the sales in million dollars to sales in labor hour $($in $000$s$)$ from Jan to Sep. $(1$pt$)$

$($b$)$ Find number of workers you need from Jan to Sep. $(1$pt$)$

$($c$)$ Find workers hired and fired from Jan to Sep. $(1$pt$)$

$($d$)$ Find beginning inventory, ending inventory, and backorders from Jan to Sep. $(1$pt$)$

$($e$)$ Based on the spreadsheet, calculate the production cost, inventory holding cost, firing cost, hiring cost, and backorder cost. $(2$pts$)$