According to automobile association of a country,on March 27,2009,the national average price per gallon of regular unleaded (87-octane)gasoline was $2.07,and the price of premium unleaded (90-octane)gasoline was $2.25.Write an objective function that models the cost of the blend of mid-grade unleaded gasoline (89-octane).
A)C = 2.25x - 2.07y
B)C = 87x + 89y
C)C = 2.07x + 2.25y
D)C = 87x + 90y
E)C = 90x + 89y

Question

According to automobile association of a country,on March 27,2009,the national average price per gallon of regular unleaded (87-octane)gasoline was $2.07,and the price of premium unleaded (90-octane)gasoline was $2.25.Write an objective function that models the cost of the blend of mid-grade unleaded gasoline (89-octane). ​
A)C = 2.25x - 2.07y
B)C = 87x + 89y
C)C = 2.07x + 2.25y
D)C = 87x + 90y
E)C = 90x + 89y

Quizplus · Accepted Answer

To find the cost of the blend of mid-grade unleaded gasoline, we need to use a weighted average. Let x represent the amount of 87-octane gasoline used and y represent the amount of 90-octane gasoline used in the blend. Since mid-grade gasoline (89-octane) is a blend of 87-octane and 90-octane gasoline, we can assume that the amounts used will add up to a fixed amount:

x + y = constant

Using this equation, we can solve for one variable in terms of the other:

y = constant - x

Substituting this into the objective function, we get:

C = 2.07x + 2.25(constant - x)

Simplifying the equation, we get:

C = 2.25x - 2.07y

Therefore, the best choice is (C).

According to Automobile Association of a Country,on March 27,2009,the National