Question $1.(60$ Points$)$

$1\mathrm{.}1.$ AvoCraft Kitchen uses high quality avocados for their meals at a rate of $50k\frac{g}{?}$ week. The Kitchen purchases each

$kg$ of avocados for $$5.$ They pay a fixed cost of $$100$ for every order they place at an avocado farm, regardless of the

size of their order. The holding cost of avocado is based on a $12\%$ annual interest rate. Assume every year is $52$ weeks.

$($a$)$ What is the economic order quantity $($EOQ$)$ for avocados? Explain what this value means.

$($b$)$ What is the time between placing two successive orders $($i$.$e$.,$ cycle time$)$ based on this EOQ?

$($c$)$ What are the annual holding and annual ordering costs for avocados based on this EOQ?

$1\mathrm{.}2.$ Suppose that the demand in $Q1\mathrm{.}1(50$ kg$/$week$)$ is in fact inaccurate and therefore, the EOQ obtained using this

demand should no longer be optimal for the kitchen $($because it is calculated using a wrong demand, and the right

demand is something else$).$ Suppose the right demand is $70k\frac{g}{?}$ week.

$($a$)$ If the Kitchen uses the EOQ calculated previously $($in Q$1\mathrm{.}1($a$))$ to place orders and does not switch to the new EOQ

that they could obtain using the right demand, what will be the total inventory cost $($with the right demand and the non$-$

optimal EOQ of Q$1\mathrm{.}1($a$))?$

$($b$)$ Compute the right EOQ under the right demand. What will the total inventory cost be if the right EOQ is used by

the Kitchen?

$($c$)$ Using the results of Q$1\mathrm{.}2($a$)$ and Q$1\mathrm{.}2($b$),$ compute the extra cost the Kitchen had to pay because of this error in

demand estimation $($i$.$e$.,$ because of using a wrong EOQ$).$

Question $2.(40$ Points$)$

A convenience store carries a certain brand of milk and sells $150$ bottles of milk per week. The annual holding cost

of one bottle of milk is $$12.$ The fixed ordering cost for any number of bottles is $$80$ per order. Once the store places

an order, it will receive the order one week later. Assume one year is $52$ weeks.

$($a$)$ Compute the inventory level at which the convenience store should place an order $($note the positive lead time$).$

$($b$)$ Compute the optimal order quantity for the milk bottles.

$($c$)$ How many times should they place an order within a year $($i$.$e$.,$ order frequency$)?$

$($d$)$ Compute the total annual inventory cost of the bottles of milk.