$(10$ points$)$ The Emerging Technologies Bank is open $24$ hours a day. Tellers work two consecutive $6-$hour shifts and are paid $$10$ an hour. THe possible shifts are as follows: midnight$-6$ a$.$m$.,6$ a$.$m$.$noon, noon$-6$ p$.$m$.,6$ p$.$m$.-$ midnight. During each shift, the following numbers of customers enter the bank:

midnight$-6$ a$.$m$.,100$

$6$ a$.$m$.-$noon, $200$

noon$-6$ p$.$m$.,300$

$6$ p$.$m$.-$ midnight, $200$

Each teller can serve up to $50$ customers per shift. To model a cost for customer impatience, we assume that any customer who is present at the end of a shift "costs" the bank $$5.$ We assume that by midnight of each day, all customers must be served, so each day's midnight$-6$ a$.$m$.$ shift begins with $0$ customers in the bank. Formulate an LP to minimize the sum of the bank's labor and customer impatience costs.

Decision variables: