To make some extra cash during the pandemic, Mark started selling musical equipment online.

To do so$,$ he typically $($i$)$ purchases premium $$bare bones$$ musical equipment from various

small manufacturers, $($ii$)$ fine$-$tunes and customizes them, and $($iii$)$ sells for a premium. He

operates his online store in a $$make$-$to$-$order$$ fashion, i$.$e$.,$ he first takes new orders and then

proceeds to buy and customize the necessary equipment.

Mark always tries to keep the price he pays for the bare$-$bones systems as low as possible.

Through skillful negotiations, he managed to convince local shops to sell him systems for around

$$5,000($per system$)$ on average. However, there is a finite supply of such systems available in

that price range $$ Mark figures around $40.$

All of Mark$$s customers come from two distinct geographical regions: the East Coast $($E$)$ and the

West Coast $($W$).$ Due to historical bias, every month, Mark first takes orders from the E and then

from the W$,$ and proceeds to fill them accordingly. For instance, if he had $30$ orders from the E

and $20$ from the W$,$ he would fill the $30$ from the E first and then only an additional $10$ from the

W due to the limited capacity.

To keep things simple, Mark typically charges the same price irrespective of the market where

the order comes from $$ currently, $$6,500$ per order. He is aware that customers typically do not

like paying for shipping. As such, he is not charging them any shipping fees beyond the base

price for the system. Based on his limited experience, he estimates that the monthly demand is:

$$ For the East Coast, expected demand is given by max$(500-0\mathrm{.}072*$ price, $0),$

$$ For the West Coast, expected demand is given by max$(600-0\mathrm{.}08*$ price, $0)$