Chapter 7 Introduction to Linear Programming MA609 Business Analytics and Data Intelligence Week 2 Solutions: The Par, Inc., is a small manufacturer of golf equipment and supplies. Par’s distributor believes a market exists for both a medium-priced golf bag, referred to as a standard model, and a high-priced golf bag, referred to as a deluxe model. A careful analysis of the manufacturing requirements resulted in the following table, which shows the production time requirements for the four required manufacturing operations and the accounting department’s estimate of the profit contribution per bag: Production Time (hours) ProductCutting and DyeingSewingFinishingInspection and packagingProfit per BagStandard7/10½11/10$10Deluxe15/62/3¼$9 The director of manufacturing estimates that 630 hours of cutting and dyeing time, 600 hours of sewing time, 708 hours of finishing time, and 135 hours of inspection and packaging time will be available for the production of golf bags during the next three months. If the company wants to maximize total profit contribution, how many bags of each model should it manufacture? Let S = number of standard bags D = number of deluxe bags Max10S+9D s.t. 7/10S+1D£630Cutting and dyeing 1/2 S+5/6D£600Sewing 1S+2/3D£708Finishing 1/10S+1/4D£135Inspection and packaging S, D ³ 0 Optimal Solution: S = 540 and D = 252 What profit contribution can Par earn on those production quantities? Profit = $7668 What is the slack time in each operation? DepartmentProduction TimeSlackCutting and Dyeing630 0Sewing480120Finishing708 0Inspection and Packaging117 18 Management of High Tech Services (HTS) would like to develop a model that will help allocate its 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. 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. Develop a linear programming model that will enable HTS to allocate technician time between regular customers and new customers. Let R = time allocated to regular customer service N = time allocated to new customer service Max0.8R+ N s.t. R+ N£ 80 25R+8N³ 800 0.6R+ N³ 0 R, N, ³ 0
