suppose the revenue in dollars from selling x cell phones is R(x)= -1.2x^2+220x. the cost in dollars of selling x cell phones is C(x)=0.05x^3-2x^2 +65x+500. find the profit function P(x)=R(x)-C(x). find the profit if x=15 hundred cell phones sold
x= 790.439875
To find the profit function P(x), subtract the cost function C(x) from the revenue function R(x):
P(x) = R(x) - C(x)
Given that R(x) = -1.2x^2 + 220x and C(x) = 0.05x^3 - 2x^2 + 65x + 500, we can substitute these values into the profit function to get:
P(x) = (-1.2x^2 + 220x) - (0.05x^3 - 2x^2 + 65x + 500)
Now we can simplify the equation:
P(x) = -1.2x^2 + 220x - 0.05x^3 + 2x^2 - 65x - 500
Combining like terms, we get:
P(x) = -0.05x^3 + 0.8x^2 + 155x - 500
To find the profit when x = 1500 (hundred cell phones sold), substitute this value into the profit function:
P(1500) = -0.05(1500)^3 + 0.8(1500)^2 + 155(1500) - 500
Calculating this expression will give you the profit when 1500 cell phones are sold.
To find the profit function, we need to subtract the cost function from the revenue function.
The revenue function is given as R(x) = -1.2x^2 + 220x.
The cost function is given as C(x) = 0.05x^3 - 2x^2 + 65x + 500.
To find the profit function P(x), we subtract C(x) from R(x):
P(x) = R(x) - C(x)
= (-1.2x^2 + 220x) - (0.05x^3 - 2x^2 + 65x + 500)
To simplify, we combine like terms:
P(x) = -1.2x^2 + 220x - 0.05x^3 + 2x^2 - 65x - 500
Now we simplify further by combining like terms:
P(x) = -0.05x^3 + 0.8x^2 + 155x - 500
To find the profit when x = 1500 cell phones sold, we substitute x = 1500 into the profit function:
P(1500) = -0.05(1500)^3 + 0.8(1500)^2 + 155(1500) - 500
Calculating this expression gives us the profit when 1500 cell phones are sold.