Question $1(10$ points$)$

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You are given the following demand forecast and operation costs information. You are also given the production schedule provided in the Table. Please calculate relevant costs for each period, and the total production costs. The calculation of the inventory cost should be based on the average inventory units. For each period, the average units in inventory is calculated as follows: $($beginning inventory $+$ ending inventory$)/2.$ Any demand that cannot be meet in each period t is placed in backorder at cost and delivered in period t$+1.$ Write your answers in the reserved spaces.

Period

Forecasted demand

$1$

$250$

$2$

$300$

$3$

$350$

$4$

$500$

$5$

$420$

$6$

$190$

Regular workforce: $$20$ per unit $(280$ units per period maximum$)$

Overtime workforce: $$30$ per unit

Beginning Inventory.: $10$

Holding cost: $$1$ per unit per period

Backorder cost: $$15$ per unit per period

The production schedule is shown in the table below:

$1$

$2$

$3$

$4$

$5$

$6$

Total

Forecasted demand

$250$

$300$

$350$

$500$

$420$

$190$

$2,010$

Regular time production

$280$

$280$

$280$

$280$

$280$

$280$

$1,680$

Overtime time production

$0$

$80$

$80$

$80$

$80$

$0$

$320$

A$)$ Write your answers in the reserved spaces about the inventory per period $($provide only the numerical value$)$

$1$

$2$

$3$

$4$

$5$

$6$

Beginning inventory $($units$)$

$10$

Ending inventory $($units$)$

Average inventory $($units$)$

Backorder inventory $($units$)$

B$)$ Write your answers in the reserved spaces about the relevant costs per period $($provide solely the numerical value without the $ sign$)$

$1$

$2$

$3$

$4$

$5$

$6$

Regular production cost

Overtime production cost

Average Inventory cost

Back orders inventory cost

C$)$ Write your answer about the total costs of the production plan in the reserved space $($provide solely the numerical value without the $ sign$)$

Total costs of the production plan