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)
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 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 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

+

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 Supe