$($please show your work$)$

$($EOQ$)$The Wallace Stationary Company purchases paper from the Seaboard Paper

Company. Wallace produces stationary that require $1,415,000$ sq$.$ yards of stationary per

year. The cost per order for the company is $$2,200$; the cost of holding $1$ yard of paper in

inventory is $$0\mathrm{.}08$ per year. Determine the following:

a$.$ Economic order quantity

B$.$ Minimum total annual cost

c$.$ Optimal number of orders per year

d$.$ Optimal time between orders

$($Quantity Discount$)$ County Hospital orders syringes from a hospital supply firm. The

hospital expects to use $40,000$ per year. The cost to order and have the syringes delivered

is $$800.$ The annual carrying cost is $$1\mathrm{.}90$ per syringe because of security and theft. The

hospital supply firm offers the following quantity discount pricing schedule.

What is best order quantity for syringes that minimize total cost?$($Newsboy model$)$ Needless Markup $($NM$),$ a famous "high end" department store, must

decide on the quantity of a high$-$priced woman's handbag to procure in Spain for the

coming Christmas season. The unit cost of the handbag to the store is $$28\mathrm{.}50$ and the

handbag will sell for $$150\mathrm{.}00.$ Any handbags not sold by the end of the season are

purchased by a liquidator for $$10\mathrm{.}00$ each. In addition, the store accountants estimate that

there is a cost of $$0\mathrm{.}40$ for each dollar tied up in inventory, as this dollar invested

elsewhere could have yielded a gross profit. Assume that this cost is attached to unsold

bags only.

a$)$ Due to the long distance and limited capacity, NM must place the order $6$ months in

advance. A detailed analysis of past data shows that if forecasting $6$ month in advance,

the number of bags sold can be described by a normal distribution, with mean $150$ and

standard deviation $60.$ What is the optimal number of bags to purchase?

b$)$ What is the expected cost of mis$-$match under the optimal purchase quantity? What is the

optimal expected profit?

c$)$ Another supplier in the US$.$ offers the same product but at a higher price of $$35$ due to its

higher production cost. For this supplier, Needless Markup only needs to place the order

$3$ months in advance which results in a much better forecast. Past data shows if ordering

$3$ months in advance, the number of bags sold can be described by a normal distribution,

with mean $150$ and standard deviation $20.$ Which supplier should NM choose?