Table $3$

$1$

$2$

$3$

$4$

$5$

$6$

Total

Inputs

Forecasted demand

$100$

$125$

$120$

$80$

$75$

$70$

$570$

Workforce Level

$80$

$80$

$80$

$80$

$80$

$80$

$480$

Part Time

$12$

$12$

$12$

$12$

$12$

$12$

$72$

Overtime

$0$

$0$

$0$

$0$

$0$

$0$

$0$

Subcontract

$0$

$0$

$0$

$0$

$0$

$0$

$0$

Derived

Beginning inventory

$20$

$12$

$0$

$0$

$0$

$0$

Ending inventory

$12$

$0$

$0$

$0$

$0$

$2$

Backlog

$0$

$21$

$49$

$37$

$20$

$0$

$127$

Calculated

Workforce level $$5$

$400$

$400$

$400$

$400$

$400$

$400$

$$2,400$

Part Time $$6$

$72$

$72$

$72$

$72$

$72$

$72$

$$432$

Overtime $$7\mathrm{.}5$

$0$

$0$

$0$

$0$

$0$

$0$

$$0$

Subcontract $$8$

$0$

$0$

$0$

$0$

$0$

$0$

$$0$

Inventory holding $$5$

$80$

$30$

$0$

$0$

$0$

$5$

$$115$

Back orders $$20$

$0$

$420$

$980$

$740$

$400$

$0$

$$2,540$

Total

$$552$

$$922$

$$1,452$

$$1,212$

$$872$

$$477$

$$5,487$

Bart Incorporated manufactures rotary air fans and uses a production$-$planning horizon of one$-$half year. It allows for regular time, part time, overtime, and subcontracting production to meet the demand but no more than $12$ units may be made by each of these methods. Both anticipation inventory and backorders are allowed. The beginning $($or current$)$ inventory is $20$ units. Their first attempt at a sales and operations plan has resulted in the following.

Use the information in Table $3.$ According to the production plan, what will be the total ending inventory in the second month after the second month's demand is satisfied?

A$)-21$ units

B$)0$ units

C$)21$ units

D$)$ This cannot be determined from the information provided.

Use the information in Table $3$ If the firm is committed to the regular production and overtime production as shown, what level of anticipation inventory would be needed at the start of the first month to result in an ending inventory of zero after month $6?$

A$)9$ or fewer units

B$)10$ units to $17$ units

C$)18$ units to $25$ units

D$)25$ units to $32$ units

Use the information in Table $3.$ According to the production plan, what is the unused overtime capacity in the fourth period?

A$)0$

B$)4$

C$)9$

D$)12$

Use the information in Table $3.$ Which of these changes would result in the greatest improvement $($in terms of total cost$)$ for the production plan?

A$)$ Increase anticipation inventory to $30$ units at the start of the first month.

B$)$ Reduce anticipation inventory to $18$ units at the start of the first month.

C$)$ Increase anticipation inventory to $40$ units at the start of the first month.

D$)$ Reduce anticipation inventory to $10$ units at the start of the first month.

Use the information in Table $3.$ Which of these changes would result in the greatest improvement $($in terms of total cost$)$ for the production plan?

A$)$ Produce an additional $12$ units using overtime in the first month.

B$)$ Produce an additional $12$ units using subcontracting in the second month.

C$)$ Produce an additional $12$ units using overtime in the third month.

D$)$ Produce an additional $12$ units using subcontracting in the fourth month.

Use the information in Table $3.$ Which of these changes would result in the greatest improvement $($in terms of total cost$)$ for the production plan?

A$)$ Increase anticipation inventory to $30$ units at the start of the first month.

B$)$ Produce an additional $12$ units using subcontracting in the second month.

C$)$ Produce an additional $12$ units using overtime in the second and third months.

D$)$ Reduce anticipation inventory to zero units at the start of the first month.

Use the information in Table $3.$ If anticipation inventory is increased to $30$ units at the start of the first month, what is the inventory holding cost over the entire planning period?

A$)$ $$115$

B$)$ $$145$

C$)$ $$185$

D$)$ $$215$

Use the information in Table $3.$ Which one of these trade$-$offs works to your greatest advantage in terms of reducing costs over the entire planning period?

A$)$ Produce units using part$-$time workers instead of regular$-$time workers.

B$)$ Begin with a larger anticipation inventory to avoid backorders completely.

C$)$ Use no overtime, subcontracting, or part time in favor of a level regular$-$capacity plan.

D$)$ Begin the planning period with $570$ units of anticipation inventory and produce nothing in the planning period.

Use the information in Table $3.$ If anticipation inventory were $30$ units at the start of the first month, what would the backorder cost be in the fourth month?

A$)$ $$840$

B$)$ $$740$

C$)$ $$640$

D$)$ $$540$

Use the information in Table $3.$ What would be the total plan cost if no more than five units each could be made each month by part$-$time, overtime, and subcontracted workers?

A$)$ $$4,920$

B$)$ $$4,822$

C$)$ $$4,775$

D$)$ $$4,550$