$[$A$]$ IPC Eagle Corporation manufactures industrial vacuum cleaners with forecasted sales for the next five weeks: Week $1=2,000$ units, Week $2=2,500,$ Week $3=3,000,$ Week $4=3,000,$ and Week $5=3,500.$ Beginning inventory equals $13,000$ units, and the firm wants to maintain this level at the end of week $5.$

A$7.$ What weekly production rate is necessary?

A$2.$ What is the ending inventory level over time using your answer in part A$1?$

$\backslash$table$[[,$Week$],[,1,2,3,4,5],[\backslash$table$[[$Beginning$],[$Inventory$]],,,,,],[+$ Producti,,,,,$],[-$ Demand,,,,,$],[\backslash$table$[[=$ Ending$],[$Inventory$]],,,,,]]$

A$3.$ Suppose

management wants to reduce its inventory level to $3,000$ units by the end of week $5$ because the chief financial officer is upset about the cost to carry so much inventory. How does the production plan and rate change?

$[$B$]$ Jet skis and snowmobiles are assembled by Mobile Incorporated. Because both end$-$items use the same small engine, you can aggregate demand for the engine assembly. Develop an aggregate plan that uses a level production strategy each quarter. What is the total cost? Assume lost sales are backordered and filled during the next quarter. Summarize the plan, its costs, and consequences using manual computations.

Initial Inventory Level

Regular Time

Lost Sales Cost$/$Unit

Inventory Carry Cost per unit

$1,000$ units

$$15$

$$24$

$$3$

$\backslash$table$[[$Quarter$,1,2,3,4,$Totals,Beginning Inventory$],[$Jet SkJ Engine,$10,000,15,000,16,000,3,000,44,000,600],[$Snowmobile Engine,$9,000,7,000,19,000,10,000,45,000,400],[$Total Englines,$19,000,22,000,35,000,13,000,89,000,1,000],[$Average Dernand Rate$/$Quarter$,,22,000$ units,,,,$],[$Regular Time Production Pate,,$22,000$ units,,,,$]]$

$[4$ points$]$