A retail store purchases computer software from a distributor for resale. For an

upcoming promotion, the retailer needs to determine the best order size for a

one$-$time purchase. One of the products is a word processing software program

that will have a special sale price of $$350.$ The retailer estimates the probabilities

for selling various quantities as follows:

Quantity Probability

$500\mathrm{.}10$

$550\mathrm{.}20$

$600\mathrm{.}20$

$650\mathrm{.}30$

$700\mathrm{.}15$

He $0\mathrm{.}051\mathrm{.}00$

The program can be purchased from the distributor for $$250$ each, but there is a

restocking charge of $20$ percent of the purchase price for the return to the distributor of any unsold programs.

What size of a purchase order should the retailer commit to$?$