Question 1 A CWD Oil 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, CWD 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. CWD Oils 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 (5 marks) b. Graph the feasible region.(4 marks) c. Determine the coordinates of each extreme point.(3 marks) d. What is the optimal solution.(3 marks) e. Solve in excel using the template provided. (5 marks)

Question B

A company produces 2 (two) different grades of gasoline regular and premium from 3(three) components (1,2,3). The company wants to determine the optimal mix of the three components in each grade of the gasoline that will maximize profit. The maximum quantities available for each component and their cost per gallon are as follows:

MGMT 2012- Introduction to Quantitative MethodsGraded Assignment One Grade S2- 2016-17- Due March 26 11.55 PM - 10 percent of Final Question 1 A CWD Oil 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, CWD 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. CWD 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 (5 marks) b. Graph the feasible region.(4 marks) c. Determine the coordinates of each extreme point.(3 marks) d. What is the optimal solution.(3 marks) e. Solve in excel using the template provided. (5 marks) Question B A company produces 2 (two) different grades of gasoline - regular and premium from 3(three) components (1,2,3). The company wants to determine the optimal mix of the three components in each grade of the gasoline that will maximize profit. The maximum quantities available for each component and their cost per gallon are as follows: Component Cost per gallon maximum gallons available per day 1 2.50 5,000 2 2.60 10,000 3 2.84 10,000 In order to ensure the appropriate blend, each grade has certain specifications as follows: Grade Component Specs Selling Price per gallon At most 30% component 1 At least 40% component 2 Regular At most 20% component 3 2.90 At least 25% component 1 At most 45% component 2 Premium At Least 30% component 3 3.00 The company wants to produce at least 10,000 gallons of each grade of gasoline. Formulate a LP model including the ratio constraints, production constraints and the objective function for this question. (20 marks) Question 2 Digital Controls, Inc. (DCI) manufactures two models of a radar gun used by police to monitor the speed of automobiles. Model A has an accuracy of plus or minus 1 mile per hour, whereas the smaller model B has an accuracy of plus or minus 3 miles per hour. For the next week, the company has orders for 100 units of model A and 150 units of model B. Although DCI purchases all the electronic components used in both models, the plastic cases for both models are manufactured at a DCI plant in Newark, New Jersey. Each model A case requires 4 minutes of injection-moulding time and 6 minutes of assembly time. Each model B case requires 3 minutes of injection-molding time and 8 minutes of assembly time. For next week, the Newark plant has 600 minutes of injection-molding time available and 1080 minutes of assembly time available. The manufacturing cost is $10 per case for model A and $6 per case for model B. Depending upon demand and the time available at the Newark plant, DCI occasionally purchases cases for one or both models from an outside supplier in order to fill customer orders that could not be filled otherwise. The purchase cost is $14 for each model A case and $9 for each model B case. Management wants to develop a minimum cost plan that will determine how many cases of each model should be produced at the Newark plant and how many cases of each model should be purchased. The following decision variables were used to formulate a linear programming model for this problem: Answer the following questions (a-i) using the output below please be brief. If there are two possible answers one will suffice. Where necessary a range analysis must be shown. a) What is the optimal solution (in words? (2 marks) b) Twenty five (25) hours of molding were lost due to machine breakdown. Evaluate the effect? Explain- ( 3 marks) c) An additional twenty hours of assembly time became available. Evaluate the effect? (3 marks) d) Demand for model A increases by 10. Evaluate the effect (3 -marks e) Suppose the purchase cost per unit for B (BP) decreased by $2. Evaluate the effect (3 marks) f) Suppose that the manufacturing cost increases to $11.20 per case for model A (AM). What is the new optimal solution? 2 marks g) Suppose that the manufacturing cost increases to $11.20 per case for model A and the manufacturing cost for model BM decreases to $5 per unit. Would the optimal solution change (use 100 percent rule) 3 marks h) Is the problem degenerate? Explain! (2 marks) i) Are there alternative optima in this problem? Explain (2 marks) Microsoft Excel 14.0 Answer Report Worksheet: [Assignment 2 S2 2014-15 solutionB.xlsx]Q1B LP formulation MAX Objective Cell (Min) Cell Name $F$3 Original Value COST Final Value 1900 2170 Variable Cells Cell Name Original Value Final Value Integer $B$2 number of units AM 100 100 Contin $C$2 number of units BM 150 60 Contin $D$2 number of units AP 0 0 Contin $E$2 number of units BP 0 90 Contin Constraints Cell Name Cell Value Formula Status Slack $F$5 Demand for model A 100 $F$5=$H$5 Binding 0 $F$6 Demand for model B 150 $F$6=$H$6 Binding 0 $F$7 Injection moulding time 580 $F$7