Apowersoft Screen Capture Pro Question B2 A refinery produces two types of gasoline product, A and B, which are blends of three crude oil ingredients (1, 2 and 3) that have different costs, sulphur percentages, octane numbers and availability. Relevant data about gasoline (final products) and crude oil (ingredients) for the current situation is given below: Product Price (/barrel) Sulphur Content Octane Demand (barrels/day) A B 669 70 At least 1% 60 At least 2% Equal to 10 Equal to 8 5,000 10,000 Ingredient Cost (/barrel) Sulphur Octane Availability (barrels/day) 1 45 0.5% 12 8,000 2 35 2% 6 2,000 3 25 3% 8 5,000 a) Formulate the problem as a linear programming problem which maximizes the total profit. Use ij as the amount of ingredient j (1, 2, 3) in product i (A, B) (e.g. A2: amount of ingredient 2 used in product A). (10 marks) After solving the problem optimally, the Excel Solver gives the following reports: After solving the problem optimally, the Excel Solver gives the following reports: Answer keport Objective Cell (Max) keport Capture Pro Cell Name $I$2 max Original Value Final Value 0 ? Variable Cells Cell Name Original Value Final Value Integer $C$15 variables A1 0 2500 Contin $D$15 variables A2 0 0 Contin $E$15 variables A3 0 2500 Contin $F$15 variables B1 0 1000 Contin $G$15 variables B2 0 2000 Contin $H$15 variables B3 0 2500 Contin Constraints Cell Name Cell Value Formula Status Slack $I$4 sulphur content A 37.5 $I$4>=$K$4 Not Binding 37.5 $I$5 sulphur content B 10 $I$5>=$K$5 Not Binding 10 $I$6 octane content A -9.09495E-13 $I$6-$K$6 Binding 0 $I$7 octane content B 0 $I$7=$K$7 Binding 0 $I$8 demand for product A 5000 $I$8 Apowersoft Sensitivity Repolpture Pro Variable Cells Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease $C$15 variables A1 2500 0 25 0 35 $D$15 variables A2 0 0 35 0 1E+30 $E$15 variables A3 2500 0 45 1E+30 0 $F$15 variables B1 1000 $G$15 variables B2 2000 0 15 1E+30 0 0 25 1E+30 0 $H$15 variables B3 2500 0 35 0 35 Constraints Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease $I$4 sulphur content A 37.5 0 0 37.5 1E+30 $I$5 sulphur content B 10 0 0 10 1E+30 $I$6 octane content A 0 3.75 0 6000 4000 $I$7 octane content B 0 3.75 0 2666.67 4000 $I$8 demand for product A 5000 17.5 5000 2000 5000 $I$9 demand for product B 5500 0 10000 1E+30 4500 $I$10 supply of ingredient 1 3500 0 8000 1E+30 4500 $I$11 supply of ingredient 2 2000 32.5 2000 1333.33 2000 $I$12 supply of ingredient 3 5000 35 5000 4500 1000 $I$12 supply of ingredient 3 5000 35 5000 4500 1000 b) In the optimal solution, how many barrels of gasoline from each type are produced? What are the amounts of ingredients for each type of gasoline? What is the optimal profit? (5 marks) c) It is proposed to introduce an environmental tax of an extra 5 per barrel produced. How can you apply this change into your mathematical model? State the change(s) needed in your mathematical model. (2 marks) d) After further investigation, you have realised you forgot to include daily production capacity of your refinery, which is 12000 barrels per day. How can you apply this change into your mathematical model? State the change(s) needed in your mathematical model. Is the optimal solution given above feasible with this new constraint? (3 marks) e) One of the customers asks for an extra 1000 barrels of gasoline A at the discounted price of 65/barrel. Justify why you should accept the deal. If you accept the deal, what will be your new profit and new production amounts if ingredient 2 has never been used in the production of product A? (5 marks) - please turn over