Chapter 5.2, Problem 49E

Management²¹ You are the service manager for a supplier of closed-circuit television systems. Your company can provide up to 160 hours per week of technical service for your customers, but the demand for technical service far exceeds this amount. As a result, you have been asked to develop a model to allocate service technicians’ time between new customers (those still covered by service contracts) and old customers (whose service contracts have expired). To ensure that new customers are satisfied with your company's service, the sales department has instituted a policy that at least 100 hours per week be allocated to servicing new customers. At the same time, your superiors have informed you that the company expects your department to generate at least $1,200 per week in revenues. Technical service time for new customers generates an average of $10 per hour (because much of the service is still under warranty), and that for old customers generates $30 per hour. How many hours per week should you allocate to each type of customer to generate the most revenue?