Bay Oil produces two types of fuels (regular and super) by mixing three ingredients. The major distinguishing feature of the two products is the octane level required. Regular fuel must have a minimum octane level of 90 while super must have a level of at least 100. The cost per barrel, octane levels and available amounts (in barrels) for the upcoming two-week period appear in the table below. Likewise, the maximum demand for each end product and the revenue generated per barrel are shown below. Ingredient Cost/Barrel Octane Available (barrels) $16.50 100 110,000 $14.00 87 350,000 $17.50 110 300,000 Revenue/ Barrel Max Demand (barrels) Regular $18.50 350,000 Super $20.00 500,000 Develop and solve a linear programming model to maximize contribution to profit. Let R; = the number of barrels of input / to use to produce Regular, / = 1, 2, 3 S; = the number of barrels of input / to use to produce Super, / = 1, 2, 3 If required, round your answers to one decimal place. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300) If the constant is "1" it must be entered in the box. Max R1 + R2 + R3 + S1 + 52 + S3 s.t. R1 S1 IA R2 + R3 + 53 5 R1 + R2 + R3 S1 + 52 + S3 R1 + R2 + 23 2 Ri + R2 + R3 S1 S2 + S3 2 S1 + S2 + S3 R1, R2, R3, 51, 52, S3 2 0 What is the optimal contribution to profit? Maximum Profit = $ by making barrels of Regular and barrels of Super