Management

quantitative approach

dont understand how to do 2-41 b) c)

/v2.cengagenow.com/ilrn/takeAssignment/takeAssignmentMain.do?invoker=&takeAssignmentSessionLocator-&inprogress-... eBook Calculator Problem 2-41 ? 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 used to produce the gasolines has a production capacity of 50,000 gallons for the next production period. Southern Oil's distributors have indicated that demand for the premium gasoline for the next production period will be at most 20,000 gallons. a. Formulate a linear programming model that can be used to 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. If required, round your answers to two decimal places. If your answer is zero, enter "0". If the constant is "1" it must be entered in the box. Let R = number of gallons of regular gasoline produced P = number of gallons of premium gasoline produced Max v 0.3 V R + 0.5 V P S.t. 0.3 V R 0.6 V PS V 18,000 Grade A crude oil available 1 V R + 1 VP = V 50,000 Production capacity 1 VP SV 20,000 Demand for premium 0 b. What is the ontimal solution? Check My Work Previous Next scar O S 06:42 p. m. 17/09/2020Gallons of regular gasoline 40,000 Gallons of premium gasoline 10,000 Total profit contribution $ 17,000 c. What are the values and interpretations of the slack variables? If an amount is zero, enter "0". Value of Slack Constraint Variable Interpretation 1 All available grade A crude oil is used 2 0 Total production capacity is used 3 10,000 Premium gasoline production is 10,000 gallons less than the maximum demand v d. What are the binding constraints? Grade A crude oil available Binding Production capacity Binding v Demand for premium Non-binding C Check My Work Previous Next0.3 VR 0.6 18-000 Gr P 50,000 Pro P 20,000 Der R, P What is the optimal solution? Gallons of regular gasoline 40,000 Gallons of premium gasoline 10,000 Total profit contribution S 17,000 c. What are the vare Jinterpretations of the slack variables? is an amount is zero, enter "0". Value of Slack Constraint Variable Interpretation 0 All available grade is 2 0 Total production capacity is used 10,000