Problems:
Linear programming
The Grand Strand Oil Company
The Grand Strand Oil Company produces regular and premium gasoline for independent service stations in the southeastern United States. The Grand Strand refinery manufactures the gasoline products by blending three petroleum components. The gasoline is sold at different prices, and the petroleum components have different costs. The firm wants to determine how to mix or blend the three components into the two gasoline products and maximize profits.
The regular gasoline can be sold for $1.00 per gallon and premium gasoline for $1.08 per gallon. For the current production planning period, Grand Strand can obtain the three petroleum components at the cost per gallon and in the quantities shown in Table1.
Product specifications for the regular and premium gasoline restrict the amounts of each component that can be used in each gasoline product. Table 2 lists the product specifications. Current commitments to distributors require Grand Strand to produce at least 10,000 gallons of regular gasoline.
The Grand Strand blending problem is to determine how many gallons of each component should be used in the regular gasoline blend and how many should be used in the premium gasoline blend. The optimal blending solution should maximize the firm's profit, subject to the constraints on the available petroleum supplies shown in Table 1, the product specifications shown in Table 2, and the required 10,000 gallons of regular gasoline.
1)Formulate and solve linear programming model that maximize the firm's profit.
2)Write a brief report that explains your findings.
Table 1. Petroleum Cost and Supply for the Grand Strand Company
|
Petroleum Component
|
Cost/Gallon
|
Maximum Available
|
|
1
|
$0.50
|
5,000 gallons
|
|
2
|
$0.60
|
10,000 gallons
|
|
3
|
$0.84
|
10,000 gallons
|
Table 2. Product Specifications for the Grand Strand Company
|
Product
|
Specifications
|
|
Regular gasoline
|
At most 30% component 1
At least 40% component 2
At most 20% component 3
|
|
Premium gasoline
|
At least 25% component 1
At most 40% component 2
At least 30% component 3
|