$5.$ Bank $24$ is open $24$ hours per day. Tellers work two consecutive $6-$hour shifts and are paid $$10$ per hour. The possible shifts are as follows: midnight$-6$ AM$,6$ AM$-$noon, noon$-6$ PM$,6$ PM$-$midnight. During each shift, the following numbers of customers enter the bank: midnight$-6$ AM$,100$; $6$ AM$-$noon, $200$; noon$-6$ PM$,300$; $6$ PM$-$midnight, $200.$ Each teller can serve up to $50$ customers per shift. To model a cost for customer impatience, we assume that any customer who is present at the end of a shift $$costs$$ the bank $$5.$ We assume that by midnight of each day, all customers must be served, so each day$$s midnight$-6$ AM shift begins with $0$ customers in the bank. Formulate an optimization problem that can be used to minimize the sum of the bank$$s labor and customer impatience costs. NOTE: The only reason the problem does not specifically ask for an LP is that the decision variables $($number of workers and customers$)$ need to be integers.