Problem $9-15$

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.

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

Let $R_i=$ the number of barrels of input i to use to produce Regular, $i=1,2,3$

$S_i=$ 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: $-300)$

$R1,R2,R3,S1,S2,S30$

What is the optimal contribution to profit?

Maximum Profit $=$$

by making

barrels of Regular and

barrels of Super.