Question

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	100	110,000
2	14	87	350,000
3	17.5	110	300,000

	Revenue/Barrel	Max Demand (barrels)
Regular	18.5	350,000
Super	20	500,000

Develop and solve a linear programming model to maximize contribution to profit

Answer 1

we want to maximize revenue and minimize cost hence

we heve to maximize

18.5(R1+R2+R3) + 20(S1+S2+S3)-16.5(R1+S1)-14(R2 +S2)-17.5(R3+S3)

= 2 R1 +4.5 R2 + R3 + 3.5 S1 + 6 S2 + 2.5 S3

using all constraints

The way to realize the maximum profit is to buy 60140.03885bbl ingredient 1, 160683.9216bbl ingredient 2, 39176.03955 ingredient 3 for regular fuel; 49859.96116bbl ingredient 1, 189316.0784bbl ingredient 2, 260823.9605bbl ingredient 3 for super f 2845000 fuel. The optimal profit is For Regular fuel Ingredient Amount 110,000 150,000 2 For Super Fuel Ingredient Amount 1 2 0 200,000 300,000