英文数学题,求高手,急A truck gets 500/x miles per gallon (mpg) when driven at a constant speed of x mph, where 40 ≤ x ≤ 80. If the price of fuel is $2.80/gal and the driver is paid $17/hr, at what speed is it most economical for the truck
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英文数学题,求高手,急A truck gets 500/x miles per gallon (mpg) when driven at a constant speed of x mph, where 40 ≤ x ≤ 80. If the price of fuel is $2.80/gal and the driver is paid $17/hr, at what speed is it most economical for the truck
英文数学题,求高手,急
A truck gets
500/x
miles per gallon (mpg) when driven at a constant speed of x mph, where
40 ≤ x ≤ 80. If the price of fuel is $2.80/gal and the driver is paid $17/hr, at what speed is it most economical for the trucker to drive? (Round your answer to two decimal places.)
英文数学题,求高手,急A truck gets 500/x miles per gallon (mpg) when driven at a constant speed of x mph, where 40 ≤ x ≤ 80. If the price of fuel is $2.80/gal and the driver is paid $17/hr, at what speed is it most economical for the truck
Let z be the total cost (a function of x) and D be the total distance (a constant),then
z = 17 * D/x + 2.8 * D/(500/x)
(The steps above are for explanation purpose only.They are not required.You can alternatively let y be the total cost per unit distance and derive the following.)
Let y (= z/D) = 17/x + 2.8x/500
Now you can minimize y,that is to find a reasonable (x,y) when the derivative of y,y',is 0.
y' = -17x^(-2) + 7/1250 = 0
x^2 = 17*1250/7
x = 55.097 = 55.10