The local supermarket buys lettuce each day to ensure really fresh produce. Each morning, any lettuce that is left from the previous day is sold to a dealer that resells it to farmers who use it to feed their animals. This week, the supermarket can buy fresh lettuce for $$5\mathrm{.}00$ a box. The lettuce is sold for $$15\mathrm{.}00$ a box and the dealer that sells old lettuce is willing to pay $$1\mathrm{.}60$ a box. Past history says that tomorrow's demand for lettuce averages $240$ boxes with a standard deviation of $36$ boxes.

How many boxes of lettuce should the supermarket purchase tomorrow $?($Use Excel's NORM.S$.$INV$()$ function to find the $z$ value. Round your answer to the nearest whole number. Enter the numbers only$)$

Inventory Management Model: Multi$-$period Model$-$ Fixed Order Quantity Model $($Q Model$)$

Item $x$ is a standard item stocked in a company's inventory of component parts. Each year the firm, on a random basis, uses about $1,500$ of item $x,$ which costs $$25$ each. Storage costs, which include insurance and cost of capital, amount to $$5$ per unit of average inventory. Every time an order is placed for more of item $x,$ it costs $$6.$

a$.$ Whenever item $x$ is ordered, what should the order size be $?($Round your answer to the nearest whole number. Enter the numbers only$)$

A

b$.$ What is the annual cost for ordering item $x?($Round your answer to the nearest whole number. Round your intermediate calculation.$)$

A

c$.$ What is the annual cost for storing item $x($Holding cost$)?($Round your answer to the nearest whole number. Round your intermediate calculation.$)$

A