1 A Southern Oil Company produces two grades of gasoline; Regular and Premium. The profit contributions are $0.30 per gallon for regular gasoline and $0.50 per gallon for premium gasoline. Each gallon of regular gasoline contains 0.3 gallons of grade A crude oil and each gallon of premium gasoline contains 0.6 gallons of grade A crude oil. For the next production period, Southern has 18,000 gallons of grade A crude oil available. The refinery that used to produce the gasoline has a production capacity if 50,000 gallons for the next production period. Southern Oils distributors have indicated that demand for the premium gasoline for the next production period will be at most 20,000 gallons.
A) Determine the number of gallons of regular gasoline and the number of gallons of premium gasoline that should be produced in order to maximize total profit contribution. Let R= number of gallons of regular gasoline produced Let P = number of gallons of premium gasoline produced.
B)What is the optimal solution?
Gallons of regular gasoline
Gallons of premium gasoline
Total profit contribution
C) What are the values and interpretations of the slack variables?
D) What are the binding constraints?
2 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 90 hours of technician time is available over the two
week planning period. To satisfy cash flow requirements, at least $850 in revenue (per technician) must be generated during the two
week period. Technician time for regular customers generates $35 per hour. However, technician time for new customers only generates an average of $7 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 80% 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.
Develop a linear programming model that will enable HTS to allocate technician time between regular and new customers.
Find the optimal solution.