1- Expedition Outfitters manufactures a variety of specialty clothing for hiking, skiing, and mountain climbing. They have decided to begin production on two new parkas designed for use in extremely cold weather: the Mount Everest Parka and the Rocky Mountain Parka. Their manufacturing plant has 120 hours of cutting time and 120 hours of sewing time available for producing these two parkas. Each Mount Everest Parka requires 30 minutes of cutting time and 45 minutes of sewing time, and each Rocky Mountain Parka requires 20 minutes of cutting time and 15 minutes of sewing time. The labor and material cost is $150 for each Mount Everest Parka and $50 for each Rocky Mountain Parka, and the retail prices through the firm's mail order catalog are $250 for the Mount Everest Parka and $200 for the Rocky Mountain Parka. Because management believes that the Mount Everest Parka is a unique coat that will enhance the image of the firm, they specified that at least 20% of the total production must consist of this model. Assuming that Expedition Outfitters can sell as many coats of each type as they can produce, how many units of each model should they manufacture to maximize the total profit contribution?
2- Management of High Tech Services (HTS) would like to develop a model that will help allocate their technicians' time between service calls to regular contract customers and new customers. A maximum of 80 hours of technician time is available over the two week planning period. To satisfy cash flow requirements, at least $800 in revenue (per technician) must be generated during the two week period.
Technician time for regular customers generates $25 per hour. However, technician time for new customers only generates an average of $8 per hour because in many cases a new customer contact does not provide billable services. To ensure that new customer contacts are being maintained, the technician time spent on new customer contacts must be at least 60% of the time spent on regular customer contacts. Given these revenue and policy requirements, HTS would like to determine how to allocate technician time between regular customers and new customers so that the total number of customers contacted during the two week period will be maximized. Technicians require an average of 50 minutes for each regular customer contact and 1 hour for each new customer contact.
A. Develop a linear programming model that will enable HTS to allocate technician time between regular customers and new customers.
B. Find the optimal solution.