Question

The profit per acre from a grove of orange trees is given by x(190 − x) dollars, where x is the number of orange trees per acre. How many trees per acre will maximize the profit?

Answer 1

Answer: 95

Step-by-step explanation: the profit function is given as

P= x (190 - x) = 190x - x²

Where x represents number of orange tree per arce.

To maximize profit, we need the maximum number of orange tree per arce to go that (r).

To get this, we get the first derivative of the profit function and equate it to zero and solve the resulting equation to get the value of x.

P = 190x - x²

dp/dx = 190 - 2x = 0

190 - 2x = 0

2x = 190

x = 190/2

x = 95

Hence 95 tress per acre will maximize profit

Answer 2

Answer:

$P(x) = 190 x -x^2$

In order to maximize the last equation we can derivate the function in term of x and we got:

$\frac{dP}{dx} = 190 -2x$

And setting this derivate equal to 0 we got:

$\frac{dP}{dx} = 190 -2x=0$

And solving for x we got:

$x = 95$

And for this case the value that maximize the profit would be x =95 and the corresponding profit would be:

$P(x=95)= 95(190-95)= 95*95 = 9025$

Step-by-step explanation:

For this case we have the following function for the profit:

$P(x) = x(190-x)$

And we can rewrite this expression like this:

$P(x) = 190 x -x^2$

In order to maximize the last equation we can derivate the function in term of x and we got:

$\frac{dP}{dx} = 190 -2x$

And setting this derivate equal to 0 we got:

$\frac{dP}{dx} = 190 -2x=0$

And solving for x we got:

$x = 95$

And for this case the value that maximize the profit would be x =95 and the corresponding profit would be:

$P(x=95)= 95(190-95)= 95*95 = 9025$