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.
a.List the linear program for this problem.
b.Use "Management Scientist" software to solve the program and report your optimal way to blend these three petroleum components for production.
c.What is the maximized profit?
Use Only a WORD file as attachment to submit your assignment. Only one attachment file (a WORD file) can be submitted for grading. You do NOT need to send in your working file from the software "Management Scientist".
You're expecting someone to do your entire assignment for you?? It won't happen here. =(
a. The linear program for this problem can be formulated as follows:
Let x1, x2, and x3 represent the number of barrels of petroleum components A, B, and C respectively to be used for blending.
Objective function:
Maximize profit = 82x1 + 88x2 + 89x3
Subject to the following constraints:
1. Availability constraint for petroleum component A:
x1 ≤ 10000
2. Availability constraint for petroleum component B:
x2 ≤ 12000
3. Availability constraint for petroleum component C:
x3 ≤ 15000
4. Blending specifications for regular grade gasoline:
0.25x1 ≤ x2 ≤ 0.30x2
No restriction on x3
5. Blending specifications for premium grade gasoline:
0 ≤ x1
0.35x2 ≤ x2
No restriction on x3
6. Blending specifications for supreme grade gasoline:
x1 ≤ 0.25x1
No restriction on x2
0.50x3 ≤ x3
b. The "Management Scientist" software can be used to solve the linear program and report the optimal way to blend the petroleum components for production.
c. The maximized profit can be obtained by evaluating the objective function at the optimal solution.