According to automobile association of a country, on March 27, 2009, the national average price per gallon of regular unleaded (85-octane) gasoline was $2.02, and the price of premium unleaded (93-octane) gasoline was $2.23.The cost of the blend of mid-grade unleaded gasoline (92-octane).Determine the constraints for the objective function.
A)x ≥ 0y ≥ 0x + y = 9285x + 93y = 92
B)x ≥ 0y ≥ 0x + y = 185x + 93y = 92
C)x ≥ 0y ≥ 0x + y = 922.02x + 2.23y = 93
D)x ≥ 0y ≥ 0x + y = 922.02x + 2.23y = 92
E)x ≥ 0y ≥ 0x + y = 922.02x + 2.23y = 85

Question

According to automobile association of a country, on March 27, 2009, the national average price per gallon of regular unleaded (85-octane) gasoline was $2.02, and the price of premium unleaded (93-octane) gasoline was $2.23.The cost of the blend of mid-grade unleaded gasoline (92-octane).Determine the constraints for the objective function. ​
A)x ≥ 0y ≥ 0x + y = 9285x + 93y = 92
B)x ≥ 0y ≥ 0x + y = 185x + 93y = 92
C)x ≥ 0y ≥ 0x + y = 922.02x + 2.23y = 93
D)x ≥ 0y ≥ 0x + y = 922.02x + 2.23y = 92
E)x ≥ 0y ≥ 0x + y = 922.02x + 2.23y = 85

Quizplus · Accepted Answer

The constraints for the objective function can be written as:
x ≥ 0 (non-negative quantity of regular gasoline)
y ≥ 0 (non-negative quantity of premium gasoline)
x + y = 185 (total quantity of mid-grade gasoline)
85x + 93y = 92(x + y) (equating the octane rating of mid-grade gasoline with the weighted average of regular and premium gasoline)
Simplifying the last equation, we get:
85x + 93y = 92x + 92y + 93y
Or, 85x = 185y
Or, x = (185/85) y
Substituting this in the second constraint, we get:
(185/85) y + y = 185
Or, y = (85/170) 185 = 92.5
Substituting this in the first constraint, we get:
x ≥ 0
Thus, the optimal solution is to have 92.5 gallons of premium gasoline and 92.5 gallons of regular gasoline to produce 185 gallons of mid-grade gasoline.

According to Automobile Association of a Country, on March 27