Humber Inc. buys items for $$45\mathrm{.}00$ each. It costs $$240\mathrm{.}00$ to place an order with the supplier. Annual demand is $18,500$ units, and the annual holding costs are charged at $25\%.$

$($a$)$ Find the economic order quantity and the optimal time between orders.

The annual number of items demanded D is:

The fixed cost per order C$0$ is:

Enter I in decimal form $($i$.$e$.0\mathrm{.}03$ instead of $3\mathrm{.}00\%)$

The annual holding cost rate I is:

The unit cost of the inventory item C is:

Round your answer for Ch to $2$ decimals.

The cost of holding one item in inventory for one year Ch is:

Round your answer for Q$$ to the nearest whole number.

The economic order quantity is Q$$ is

Round your answer for T$$ to the nearest whole number.

The optimal time $($in days$)$ between orders is T$$ is

$($b$)$ Find the total annual relevant cost.

Round your answer for TC$($Q$)$ to $2$ decimal places.

The total annual relevant cost TC$($Q$)$ is

$($c$)$ Suppose Humber decided to operate with backorders $($planned shortages$).$ Say, the backordering costs are estimated to be $$6\mathrm{.}00$ per unit per year. Find the economic order quantity and the maximum number of backorders.

The cost of backordering one item for one year Cb is:

Round your answer for Q$$ to the nearest whole number.

The economic order quantity is Q$$ is

Round your answer for S$$ to the nearest whole number.

The maximum number of back orders S$$ is

$($d$)$ Find the total annual relevant cost with backorders $($planned shortages$).$ How do you think, should the company use the backorder inventory policy or not? Why?

Round your answer for TC$($Q$,$S$)$ to $2$ decimal places.

The total annual cost TC$($Q$,$S$)$ for the inventory model with backorders is

Your final conclusion is

The company technically can not use the backorder policy as the total annual relevant cost drops if such policy is introduced.

The company technically can use the backorder policy as the total annual relevant cost increases if such policy is introduced.

The company technically can use the backorder policy as the total annual relevant cost drops if such policy is introduced.

The company technically can not use the backorder policy as the total annual relevant cost increases if such policy is introduced.

None of the above.