PA $13-5($Algo$)$ Teddy Bower is an outdoor clothing and accessories chain...

Teddy Bower is an outdoor clothing and accessories chain that purchases a line of parkas at $$11$ each from its Asian supplier, TeddySports. Unfortunately, at the time of the order placement, demand is still uncertain: Teddy Bower forecasts that its demand is normally distributed with a mean of $2,200$ and a standard deviation of $1,300.$ Teddy Bower sells these parkas at $$24$ each. Unsold parkas have little salvage value; Teddy Bower simply gives them away to a charity $($and also doesn$$t collect a tax benefit for the donation$).$ Use Table $13\mathrm{.}4.$

Note: Do not round intermediate calculations. If a part of the question specifies whether to use Table $13\mathrm{.}4,$ or to use Excel, then credit for a correct answer will depend on using the specified method.

How many parkas should Teddy Bower buy from TeddySports to maximize expected profit? Use Table $13\mathrm{.}4$ and the round$-$up rule.

Note: Enter your answer as a whole number.

If Teddy Bower orders $3,000$ parkas, what is expected leftover inventory? Use Table $13\mathrm{.}4$ and the round$-$up rule.

Note: Round your answer to $2$ decimal places.

Table $13\mathrm{.}4$

TABLE $13\mathrm{.}4$

The Distribution, $F(Q),$ and Expected Inventory, $I(Q),$ Functions for the Standard Normal Distribution

Function

$\backslash$table$[[-1\mathrm{.}6,0\mathrm{.}0548,0\mathrm{.}0232],[-1\mathrm{.}5,0\mathrm{.}0668,0\mathrm{.}0293],[-1\mathrm{.}4,0\mathrm{.}0808,0\mathrm{.}0367],[-1\mathrm{.}3,0\mathrm{.}0968,0\mathrm{.}0455],[-1\mathrm{.}2,0\mathrm{.}1151,0\mathrm{.}0561],[-1\mathrm{.}1,0\mathrm{.}1357,0\mathrm{.}0686],[-1\mathrm{.}0,0\mathrm{.}1587,0\mathrm{.}0833],[-0\mathrm{.}9,0\mathrm{.}1841,0\mathrm{.}1004],[-0\mathrm{.}8,0\mathrm{.}2119,0\mathrm{.}1202],[-0\mathrm{.}7,0\mathrm{.}2420,0\mathrm{.}1429],[-0\mathrm{.}6,0\mathrm{.}2743,0\mathrm{.}1687],[-0\mathrm{.}5,0\mathrm{.}3085,0\mathrm{.}1978],[-0\mathrm{.}4,0\mathrm{.}3446,0\mathrm{.}2304],[-0\mathrm{.}3,0\mathrm{.}3821,0\mathrm{.}2668],[-0\mathrm{.}2,0\mathrm{.}4207,0\mathrm{.}3069],[-0\mathrm{.}1,0\mathrm{.}4602,0\mathrm{.}3509],[0\mathrm{.}0,0\mathrm{.}5000,0\mathrm{.}3989],[0\mathrm{.}1,0\mathrm{.}5398,0\mathrm{.}4509],[0\mathrm{.}2,0\mathrm{.}5793,0\mathrm{.}5069],[0\mathrm{.}3,0\mathrm{.}6179,0\mathrm{.}5668],[0\mathrm{.}4,0\mathrm{.}6554,0\mathrm{.}6304],[0\mathrm{.}5,0\mathrm{.}6915,0\mathrm{.}6978],[0\mathrm{.}6,0\mathrm{.}7257,0\mathrm{.}7687],[0\mathrm{.}7,0\mathrm{.}7580,0\mathrm{.}8429],[0\mathrm{.}8,0\mathrm{.}7881,0\mathrm{.}9202],[0\mathrm{.}9,0\mathrm{.}8159,1\mathrm{.}0004],[1\mathrm{.}0,0\mathrm{.}8413,1\mathrm{.}0833],[1\mathrm{.}1,0\mathrm{.}8643,1\mathrm{.}1686],[1\mathrm{.}2,0\mathrm{.}8849,1\mathrm{.}2561],[1\mathrm{.}3,0\mathrm{.}9032,1\mathrm{.}3455],[1\mathrm{.}4,0\mathrm{.}9192,1\mathrm{.}4367],[1\mathrm{.}5,0\mathrm{.}9332,1\mathrm{.}5293],[1\mathrm{.}6,0\mathrm{.}9452,1\mathrm{.}6232]]$