Seastrand Oil Company produces two grades of gasoline: regular and high octane.
ID: 460760 • Letter: S
Question
Seastrand Oil Company produces two grades of gasoline: regular and high octane. Both gasolines are produced by blending two types of crude oil. Although both types of crude oil contain the two important ingredients required to produce both gasolines, the percentage of important ingredients in each type of crude oil differs, as does the cost per gallon. The percentage of ingredients A and B in each type of crude oil and the cost per gallon are shown.
Each gallon of regular gasoline must contain at least 60% of ingredient A, whereas each gallon of high octane can contain at most 30% of ingredient B. Daily demand for regular and high-octane gasoline is 900000 and 500000 gallons, respectively. How many gallons of each type of crude oil should be used in the two gasolines to satisfy daily demand at a minimum cost? Round your answers to the nearest whole number. Round the answers for cost to the nearest dollar.
Crude Oil Cost Ingredient A Ingredient B 1 $0.15 40% 40% 2 $0.20 70% 10%Explanation / Answer
As the demand has to be satisfies at minimum cost, the objective is to use the minimum amount of Crude Oil 2.
For regular gasoline,
Let 1 gallon of Crude Oil 2 be mixed with x gallons of crude oil 2
For the minimum cost, it must contain 60% of ingredient A.
Thus,
1*0.7 + x*0.4 = 0.6 (1+x)
Thus x = (0.7-0.6)/ (0.6 – 0.4) = 0.5
Thus, 1.5 gallons of Regular gasoline needs 0.5 Gallons of Crude Oil 1 and 1 gallon of crude oil 2.
Thus, 900000 gallons of regular gasoline need 300000 gallons of crude 1 and 600000 gallons of crude 2.
For high octane gasoline,
Let 1 gallon of crude 2 be mixed with y gallons of crude 1.
Thus,
1*0.1 + y*0.4 = 0.3*(1+y)
Thus, y = (0.3-0.1)/ (0.4-0.3) = 2
Thus 3 gallons of high octane gasoline needs 2 Gallons of Crude 1 and 1 Gallon of crude 2
Thus, 500000 gallons of high octane gasoline need 333333 gallons of crude 1 and 166667 gallons of crude 2.
Total amount of crude 1 = 633333 gallons
Total amount of crude 2 = 766667 gallons
Total Cost = 0.15 (633333) + 0.2 (766667) = $ 248333
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