Your company produces three grades of gasolines for industrial distribution. The three grades- premium, regular and...

 

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Your company produces three grades of gasolines for industrial distribution. The three grades- premium, regular and economy-are produced by refining a blend of three types of crude oil: Brent, Dubai and WTI. Each crude oil differs not only in cost per barrel, but in its composition as well. Table 1 below indicates the percentage of three crucial compounds found in each of the crude oils, the cost per barrel for each, and the maximum weekly availability of each. Table 1: Ingredient Data Crude Compound A Oil Type Brent Dubai WTI (%) 35 50 60 Compound B Compound C Cost/Barrel (%) (%) 25 35 30 15 20 15 Table 2: Gasoline Data Gasoline Type Premium Regular Economy Compound A Table 2 indicates the weekly demand for each grade of gasoline and the specific conditions on the amounts of the different compounds that each grade of gasoline should contain. The table shows, for example, that in order for gasoline to be classified as premium grade, it must contain at least 55% of compound A, no more than 23% of compound B and no restrictions on compound C. Your company must decide how many barrels of each type of crude oil to buy each week for blending to satisfy demand at minimum cost. ≥ 55% ≥ 40% Compound B ($) 86 92 95 ≤ 23% ≥ 25% Availability (barrels) ≤ 35% ≤ 25% 15,000 32,000 24,000 Compound C Demand (barrels) 14,000 22,000 25,000 a. Which constraint(s) should you remove from your LP in Q1? b. Set up the corresponding LP in Excel and run Solver. 1. Write down the linear program to determine the optimal blending plan. (8 marks) 2. Set up the Excel spreadsheet and use Solver to compute the optimal plan. Interpret your Solver's answer report. (8 marks) 3. Your company finds a new crude oil supplier who can sell you unlimited Brent oil at current cost. Your company produces three grades of gasolines for industrial distribution. The three grades- premium, regular and economy-are produced by refining a blend of three types of crude oil: Brent, Dubai and WTI. Each crude oil differs not only in cost per barrel, but in its composition as well. Table 1 below indicates the percentage of three crucial compounds found in each of the crude oils, the cost per barrel for each, and the maximum weekly availability of each. Table 1: Ingredient Data Crude Compound A Oil Type Brent Dubai WTI (%) 35 50 60 Compound B Compound C Cost/Barrel (%) (%) 25 35 30 15 20 15 Table 2: Gasoline Data Gasoline Type Premium Regular Economy Compound A Table 2 indicates the weekly demand for each grade of gasoline and the specific conditions on the amounts of the different compounds that each grade of gasoline should contain. The table shows, for example, that in order for gasoline to be classified as premium grade, it must contain at least 55% of compound A, no more than 23% of compound B and no restrictions on compound C. Your company must decide how many barrels of each type of crude oil to buy each week for blending to satisfy demand at minimum cost. ≥ 55% ≥ 40% Compound B ($) 86 92 95 ≤ 23% ≥ 25% Availability (barrels) ≤ 35% ≤ 25% 15,000 32,000 24,000 Compound C Demand (barrels) 14,000 22,000 25,000 a. Which constraint(s) should you remove from your LP in Q1? b. Set up the corresponding LP in Excel and run Solver. 1. Write down the linear program to determine the optimal blending plan. (8 marks) 2. Set up the Excel spreadsheet and use Solver to compute the optimal plan. Interpret your Solver's answer report. (8 marks) 3. Your company finds a new crude oil supplier who can sell you unlimited Brent oil at current cost.