Bay Oil produces two types of fuels (regular and super) bymixing three ingredients. The major distinguishing feature of thetwo products is the octane level required. Regular fuel must have aminimum octane level of 90 while super must have a level of atleast 100. The cost per barrel, octane levels and available amounts(in barrels) for the upcoming two-week period appear in the tablebelow. Likewise, the maximum demand for each end product and therevenue generated per barrel are shown below.
| Ingredient | Cost/Barrel | Octane | Available (barrels) |
| 1 | $16.50 | 100 | 110,000 |
| 2 | $14.00 | 87 | 350,000 |
| 3 | $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 maximizecontribution to profit.
| Let | Ri = the number of barrels of input i to useto produce Regular, i = 1, 2, 3 |
| Si = the number of barrels of input i to useto produce Super, i = 1, 2, 3 |
If required, round your answers to one decimal place. Forsubtractive or negative numbers use a minus sign even if there is a+ sign before the blank. (Example: -300) If the constant is \"1\" itmust be entered in the box.
| 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   barrelsof Regular and   barrels of Super.
