Riverside oil company in eastern Kentucky produces 3 different grades of gasoline. They are regular, premium, and supreme grades. Each barrel of regular grade sells for $82 while premium grade sells for $88 per barrel and supreme grade sells for $89 per barrel. Petroleum component A, B, and C are purchased to be blended together for the production of three different grades of gasoline. The availability and cost of petroleum components A, B, and C are given in the following table.
|
Petroleum Component
|
Barrels available
|
Cost per Barrel
|
|
A
|
10000
|
$32
|
|
B
|
12000
|
$45
|
|
C
|
15000
|
$39
|
Also, the blending specifications for these three grades of gasoline are as follows:
|
Product
|
Blending Specification
|
|
Regular
|
at least 25% of A; no more than 30% of B; no restriction on C
|
|
Premium
|
at least 35% of B; no restriction on A and C
|
|
Supreme
|
no more than 25% of A; no restriction on B; at least 50% on C
|
Our goal is to maximize the profit from this production process.
- List the linear program for this problem.
- Use "LINGO" software to solve the program and report your optimal way to blend these three petroleum components for production.
- What is the maximized profit?