Consider the problem of formulating an LP where for the production of three grades gasoline, gas1, gas2 and gas3 sold at $90, $ 118 and $ 130 per barrel; the minimum required octane rating are respectively 87, 89 and 92. The manufacturer uses three crudes; crude 1, crude 2 and crude 3, with octane ratings respectively as follows: 70, 80, and 98. There are 190 barrels of crude 1 available, 150 barrels of crude 2 available and 90 barrels of crude 3 available. The production of gas3 should not exceed 20 barrels.

Define the decision variables: and formulate the problem as an LP to maximize revenue. Implement the LP on Excel and give (a) optimal solution, (b) optimal value and (c) shadow prices of each constraint. Name the constraint by what it refers to. (20 + 10 =30 points)