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 are shown in the following table. Likewise, the maximum demand for each end product and the revenue generated per barrel are shown. Input Cost/Barrel Octane Available (barrels) 1 $16.5 92 130,000 2 $15 85 330,000 3 $17.5 105 320,000 Revenue/Barrel Max Demand (barrels) Regular $18.5 340,000 Super $22 490,000 Develop and solve a linear programming model to maximize contribution to profit. Let Ri = the number of barrels of input i to use to produce Regular, i=1,2,3 Si = the number of barrels of input i to use to produce Super, i=1,2,3 If required, round your answers to two decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300) Max R1 + R2 + R3 + S1 + S2 + S3 s.t. R1 + S1 ? R2 + + S2 ? R3 + S3 ? R1 + R2 + R3 ? S1 + S2 + S3 ? R1 + R2 + R3 ? R1 + R2 + R3 S1 + S2 + S3 ? S1 + S2 + S3 R1, R2, R3, S1, S2, S3 ? 0 What is the optimal contribution to profit? Maximum Profit = $[ ? ] by making [ ? ] barrels of Regular and [ ? ] barrels of Super.