Acar rental agency rents 190 cars per day at a rate of 29 dollars per day. for each 1 dollar increase in the daily rate, 5 fewer cars are rented. at what rate should the cars be rented to produce the maximum income, and what is the maximum income?

The equation that we can create from this situation is:

i = (190 – 5 x) * (29 + x)

where i is the income and x is the increase in daily rate

Expanding the equation:

i = 5510 + 190x – 145x - 5x^2

i = -5x^2 + 45x + 5510

Taking the 1st derivative:

di/dx = -10x +45

Set to zero to get the maxima:

-10x + 45 = 0

x = 4.5

So the cars should be rented at:

29 + x = 33.5 dollars per day

The maximum income is:

i = (190 – 5*4.5) * (33.5)

i = 5,611.25 dollars

solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.

answer: what is the question you're trying to ask?

step-by-step explanation: