Riverside Oil Company in eastern Kentucky produces regular, midgrade and supreme gasoline.

Riverside Oil Company in eastern Kentucky produces regular, midgrade and supreme gasoline. The required octane rating for the regular product must be between 85 and 86 (so its rating must be no less than 85 and no more than 86); for the midgrade product must be between 87.5 and 88.5; and for the supreme product must be between 90 and 91. The selling price for each of the 3 gasoline products (gasolines) is given in the Riverside sheet of the accompanying Excel file. Each of these types of gasoline is manufactured by mixing different quantities of three inputs (raw materials), the characteristics of which are also given in the Riverside sheet.

In order to meet demand, Riverside needs to make at least 400,000 barrels of regular, 300,000 barrels of midgrade and 350,000 barrels of supreme. How should the company allocate the available inputs to the production of regular and supreme gasolines if they want to maximize profits while achieving the desired octane levels? Using Solver Simplex Method

Input
1
2
3
Gasoline
Regular
Midgrade
Supreme

Cost per Barrel
Octane Rating
$17.25
85
$15.75
83
$17.75
92

Barrels Available (in 1000s)
300
450
550

Octane RatingSelling price ($Required Production (in 1000)
400
Between 85 an $19.00
$27.00
300
Between 87.5
350
Between 90 an $33.00