According to automobile association of a country,on March 27,2009,the national average price per gallon of regular unleaded (88-octane)gasoline was $2.08,and the price of premium unleaded (93-octane)gasoline was $2.27.Write an objective function that models the cost of the blend of mid-grade unleaded gasoline (89-octane).What is the optimal cost?
A)$2.23/gal
B)$1.66/gal
C)$2.12/gal
D)$3.12/gal
E)$3.23/gal

Question

According to automobile association of a country,on March 27,2009,the national average price per gallon of regular unleaded (88-octane)gasoline was $2.08,and the price of premium unleaded (93-octane)gasoline was $2.27.Write an objective function that models the cost of the blend of mid-grade unleaded gasoline (89-octane).What is the optimal cost? ​
A)$2.23/gal
B)$1.66/gal
C)$2.12/gal
D)$3.12/gal
E)$3.23/gal

Quizplus · Accepted Answer

Let x be the price of mid-grade unleaded gasoline per gallon. To find the cost of the blend, we can set up a weighted average: 
(0.5)(2.08) + (0.5)(x) = 2.12 
This is because we want the blend to be halfway between the prices of regular and premium gasoline, and we know the average is $2.12 per gallon. Solving for x, we get: 
0.5x = 2.12 - 1.04 
0.5x = 1.08 
x = $2.16 per gallon 
Therefore, the optimal cost for the blend of mid-grade unleaded gasoline is $2.16 per gallon, which is closest to choice C: $2.12/gal.

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