A company produces 2 (two) different grades of gasoline – regular and premium fr

Question

A company produces 2 (two) different grades of gasoline – regular and premium from 3(three) components (1,2,3). The company wants to determine the optimal mix of the three components in each grade of the gasoline that will maximize profit. The maximum quantities available for each component and their cost per gallon are as follows: Component Cost per gallon maximum gallons available per day 1 2.50 5,000 2 2.60 10,000 3 2.84 10,000 In order to ensure the appropriate blend, each grade has certain specifications as follows: Grade Component Specs Selling Price per gallon Regular At most 30% component 1 At least 40% component 2 At most 20% component 3 2.90 Premium At least 25% component 1 At most 45% component 2 At Least 30% component 3 3.00 The company wants to produce at least 10,000 gallons of each grade of gasoline. Formulate a LP model including the ratio constraints, production constraints and the objective function for this question. (20 marks)

Explanation / Answer

xij = barrels of component i used in grade j per day

Objective function:

Maximize z = 2.90 (x1R + x2R + x3R) + 3.00 (x1P + x2P + x3P) – 2.50 (x1R + x1P) – 2.60 (x2R + x2P) – 2.84 (x3R + x3P)

Constraints:

Production constraints:

x1R + x1P 5,000

x2R + x2P 10,000

x3R + x3P 10,000

Ratio constraints:

(1) x1R / (x1R + x2R + x3R)   0.30

(2) x2R / (x1R + x2R + x3R)   0.40

(3) x3R / (x1R + x2R + x3R)   0.20

(4) x1P / (x1P + x2P + x3P) 0.25

(5) x2P / (x1P + x2P + x3P)   0.45

(6) x3P / (x1P + x2P + x3P) 0.30

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