You are in charge of managing the inventory of cookie boxes for Kristen$$s cookie$-$making business.

The flow rate of the process is constant and equal to $6$ orders per hour. Assume the process goes

on forever without interruption and that each order uses exactly one cookie box. You purchase

the cookie boxes from a supplier who delivers them to you exactly two days after you have placed

an order. He charges $80$ cents per box plus delivery fee of $$10($no matter how many boxes were

ordered$).$ The storage costs amount to $28$ cents a box per day. The cost of electricity for Kristen$$s

dorm room is a fixed $$50$ per month $($irrespective of actual consumption$).$ Kristen gets a $2\%$

interest rate on her savings$$ account annually. She plans to invest any cash the cookie business

generates into an exciting business opportunity promising a return on investment of $7\%$ per week.

Assume $24$ hours a day and $7$ days a week.

$($a$)$ List the values for the relevant parameters for the Economic Order Quantity $($EOQ$)$ model,

namely, the unit purchasing cost $($C$),$ the demand rate $($D$),$ the cost of capital $($i$),$ the

inventory holding cost $($H$),$ the setup cost $($S$)$ and the lead time $($L$).$

$($b$)$ Kristen tells you that you should order once a week, that you should order exactly the

quantity needed to satisfy demand between two orders, and that you should place orders at

the right time so the delivery arrives just as you run out of cookie boxes. What is your total

average daily cost $($setup $+$ inventory holding $+$ purchasing$)?$

$($c$)$ How often should you place an order in order to minimize total cost per day? What will be

your total cost per day in that case?

$($d$)$ Suppose your supplier refuses to deliver orders for less than $300$ boxes. How often should

you place an order then? Explain why. By how much does this constraint increase your

total cost per day compared to the minimum possible value?