The hourly profit ($P) obtained from operating a fleet of n taxis is given by
P=-2n^2+84n-45
What is the profit if 20 taxis are on the road?
What is the maximum hourly profit?
What number of taxis gives the max hourly profit?
How much money is lost per hour if no taxis are on the road?
P(20) = -2(400) + 84(20) - 45
if you do not know calculus, find vertex of parabola by completing square. I am assuming calculus.
0 = -4 n + 84
n = 21 at maximum
so
Pmax = -2(21^2) + 84(21) - 45
21, been there, did that
-45 when n = 0
bhj
To find the profit when 20 taxis are on the road, substitute n=20 into the profit function P=-2n^2+84n-45:
P = -2(20)^2 + 84(20) - 45
P = -2(400) + 1680 - 45
P = -800 + 1680 - 45
P = 835.
Therefore, the profit when 20 taxis are on the road is $835.
To find the maximum hourly profit, we need to find the vertex of the quadratic function. The formula for the x-coordinate of the vertex of a quadratic function in the form ax^2 + bx + c is given by x = -b/(2a).
For the profit function P=-2n^2+84n-45, a = -2 and b = 84. Using the formula:
n = -84/(2(-2))
n = -84/-4
n = 21.
Therefore, the maximum hourly profit is achieved when there are 21 taxis on the road.
To find the number of taxis that gives the maximum hourly profit, we use the value of n from the previous step, which is 21.
Therefore, the number of taxis that gives the maximum hourly profit is 21.
To find the amount of money lost per hour if no taxis are on the road, substitute n=0 into the profit function P=-2n^2+84n-45:
P = -2(0)^2 + 84(0) - 45
P = -45.
Therefore, if no taxis are on the road, the company loses $45 per hour.
To find the profit when 20 taxis are on the road, substitute the value of 20 into the equation for P:
P = -2(20)^2 + 84(20) - 45
Simplifying the equation will give you the profit when 20 taxis are on the road.
To find the maximum hourly profit, you can use the vertex formula. The vertex formula states that the x-coordinate of the vertex of a quadratic equation in the form of ax^2 + bx + c can be found using the formula: x = -b/2a. In this case, the equation is:
P = -2n^2 + 84n - 45
Using the vertex formula, you can determine the number of taxis that will give the maximum hourly profit.
To find out the number of taxis that gives the maximum hourly profit, you need to find the x-coordinate of the vertex, which represents the number of taxis. Using the formula x = -b/2a with the equation P = -2n^2 + 84n - 45, you can calculate the number of taxis that will maximize the profit.
To find out how much money is lost per hour if no taxis are on the road, you need to substitute the value of 0 for n in the profit equation:
P = -2(0)^2 + 84(0) - 45
Simplifying the equation will give you the amount of money lost per hour with no taxis on the road.