Creative Sports Design (CSD) manufactures a standard-size racket and an oversize racket. The firm’s rackets are extremely light due to the use of a magnesium-graphite alloy. Each standard-size racket uses 0.125 kilograms of the alloy and each oversize racket uses 0.4 kilograms; over the next two-week production period only 80 kilograms of the alloy are available. Each standard-size racket uses 10 minutes of manufacturing time and each oversize racket uses 12 minutes. Also, 40 hours of manufacturing time are available each week. The profit contributions are $10 for each standard-size racket and $15 for each oversize racket. How many rackets of each type should CSD manufacture over the next two weeks to maximize the total profit contribution? 

a. Define decision variables and formulate the problem. 

b. Solve the problem using the graphical method.

1.4 Management of High Tech Services (HTS) would like to develop a model that will help allocate their technician’s 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. To ensure that new customer contracts are being maintained, the technician time spent on new customer contracts must be at least 60% of the time spent on regular customer contracts. 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 contracted during the two-week period will be maximized. Technicians require an average of 50 minutes for each regular customer contract and 1 hour for each new customer contract. 

a. Develop a linear programming model for the problem. 

b. Find the optimal solution via Excel

Industrial Designs has been awarded a contract to design a label for a new wine produced by Lake View Winery. The company estimates that 150 hours will be required to complete the project. The firm’s three graphics designers available for assignment to this project are Lisa, a senior designer and team leader; David, a senior designer; and Sarah, a junior designer. Because Lisa has worked on several projects for Lake View Winery, management specified that Lisa must be assigned at least 40% of the total number of hours assigned to the two senior designers. To provide a label-designing experience for Sarah, Sarah must be assigned at least 15% of the total project time. However, the number of hours assigned to Sarah must not exceed 25% of the total number of hours assigned to the two senior designers. Due to other project 2commitments, Lisa has a maximum of 50 hours available to work on this project. Hourly wage rates are $30 for Lisa, $25 for David, and $18 for Sarah.

a. Formulate a linear program that can be used to determine the number of hours each graphic designer should be assigned to the project in order to minimize total cost. 

b. How many hours should each graphic designer be assigned to the project? What is the total cost? 

c. Suppose Lisa could be assigned more than 50 hours. What effect would this have on the optimal solution? Explain.

d. If Sarah were not required to work a minimum number of hours on this project, would the optimal solution change? Explain