The owner of a food cart must balance the advantage of speeding up service so as to be able to serve more customers with the disadvantage of having to pay for that speedup. During the busy lunch period there is an average arrival rate of .5 customers per minute. Customers who arrive when there are 4 people waiting will depart unserved. Those who are served spend a random amount with average $8. By using such efficiencies as updating equipment, hiring support servers, and streamlining processes, the operator can increase the service rate from its current level of one customer per 2.5 minutes, but we assume that the operating costs grow proportionally to the service rate, with proportionality constant 3. Find the optimal service rate, and the amount by which net profit per hour can be increased by using this service rate.

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