Formulate a linear program? A corporation that produces gasoline and oil special

Question

Formulate a linear program?
A corporation that produces gasoline and oil specialty additives purchases three grades of petroleum distillates, A, B,
and C. The company then combines the three according to specifications of the maximum or minimum percentages
of grades A or C in each blend.
Mixture/ Max% allowed for Additive A/ Min % allowed for Additive C/ $/gallon
Deluxe/ 60%/ 20%/ 7.9
Standard/ 15%/ 60%/ 6.9
Economy/ — /50%/ 5.0
Supplies of the three basic additives and their costs are:
Maximum quantity Cost
Distillate/ available per day (gals)/ $/gallon
A/ 4000/ 0.60
B/ 5000/ 0.52
C/ 2500/ 0.48
Show how to formulate a linear program to determine the production policy that will maximize profits.

Explanation / Answer

I think the problem statements below in terms of A and C are backwards, it should be minimum percent max % of C (the cheap fuel) and min % of A, the expensive fuel) but I am solving them as written. Just switch the order of the variables if you have this confirmed. I will put after the statement what I think it should be in parentheses. Let's label Deluxe D, Standard S, and Economy E Then, max 7.9 D + 6.9S + 5.0 E - .6A - .52B - .48C (this uses sales prices and materials costs) subject to A + B + C - D - S - E >= 0 (purchase at least as much as sell; perhaps, make this an equality) Fuel requirements for each grade: .6 D + .15 S - A >= 0 max % of A C - .2D - .6S - .5 E >= 0 (I think these two should be A - .6D - .15S >= 0 and .2D+.6S + .5E - C >= 0) Quantities available: A

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