$($Comprehensive EOQ calculations$)$ Knutson Products Inc. is involved in the production of airplane parts and has the following inventory, carrying, and storage costs:

Orders must be placed in round lots of $100$ units.

Annual unit usage is $300,000.($Assume a $50-$week year in your calculations.$)$

The carrying cost is $15$ percent of the purchase price.

The purchase price is $$20$ per unit.

The ordering cost is $$500$ per order.

The desired safety stock is $3,000$ units. $($This does not$-$include delivery$-$time stock.$)$

The delivery time is $5$ week.

Given the foregoing information:

a$.$ Determine the optimal EOQ level.

b$.$ How many orders will be placed annually?

c$.$ What is the inventory order point? $($That is$,$ at what level of inventory should a new order be placed?$)$

d$.$ What is the average inventory level?

e$.$ What would happen to the EOQ if annual unit sales doubled $($all other unit costs and safety stocks remaining constant$)?$ What is the elasticity of EOQ with respect to sales? $($That is$,$ what is the percentage change in EOQ divided by the percentage change in sales?$)$

f$.$ If carrying costs double, what will happen to the EOQ level? $($Assume the original sales level of $300,000$ units.$)$ What is the elasticity of EOQ with respect to carrying costs?

g$.$ If the ordering costs double, what will happen to the level of EOQ? $($Again$,$ assume original levels of sales and carrying costs.$)$ What is the elasticity of EOQ with respect to ordering costs?

h$.$ If the selling price doubles, what will happen to EOQ? What is the elasticity of EOQ with respect to selling price?