S.O.C. produces 2 grades of gas:regular & premium.

Let x = regular. Let y = premium.
$\displaystyle {\color{red}x \ge 0}$

$\displaystyle {\color{red}y \ge 0}$

The profit contributions are $0.30/gal for regular and $0.50/gal for premium.

P(x, y) = .3x + .5y
Each gallon of regular gas contains 0.3 gal of grade A crude oil and each gal of premium gas contains 0.6 gal of grade A crude oil.

For the next production period, S.O.C. has 18,000 gal of grade A crude oil available.

$\displaystyle {\color{red}.3x+.6y \leq 18000}$
The refinery used to produce the gasolines has a production capacity of 50,000 gal for the next production period.

$\displaystyle {\color{red}x+y \leq 50000}$
S.O.C.'s distributors have indicated that demand for the premium gas for the next production period will be at most 20,000 gallons.

$\displaystyle {\color{red}y \leq 20000}$

a)Formulate a linear programming model that can be used to determine the # of gallons of regular gasoline and the number of gallons of premium gasoline that should be produced in order to maximize total profit contribution.

b)What is the optimal solution?

c)What are the values and interpretations of the slack variables?

d)What are the binding constraints?