Derivative: finding profit equation; maximizing profit

K

kjones

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The question is:

The revenue (in dollars) from the dale of "x" dinners is given by:

. . .R(x) = -0.00000183x^3 - 0.00029532x^2 + 30.1898x

and the cost (in dollars) of producing "x" dinners is given by the function:

. . .C(x) = -0.001x^2 + 11x + 13000

a) I need to find an equation for profit as a function of the number of dinners sold.

b) I need to find the profit when 2300 dinners are sold.

c) I need to use a derivative to find how many dinners need to be sold to maximize profit. What is the maximum profit?

THANKS~

K
 
Re: Derivative

kjones said:
The question is:

The revenue (in dollars) from the dale of "x" dinners is given by:

R (x) = -0.00000183x^3 - 0.00029532x^2 + 30.1898x

and the cost (in dollars) of producing "x" dinners is given by the function:

C (x) = -0.001x^2 + 11x + 13000




a) I need to find an equation for profit as a function of the number of dinners sold.

this is easy ... Profit = Revenue - Cost

b) I need to find the profit when 2300 dinners are sold.

evaluate your profit function found in part a) for x = 2300

c) I need to use a derivative to find how many dinners need to be sold to maximize profit. What is the maximum profit?

take the derivative of your profit function, set it equal to 0, and maximize

K
Click to expand...
 
the profit function is just a basic polynomial ... show me its derivative and I'll help with the maximization.
 
In part a):

I need to find an equation for profit as a function of the number of dinners sold.

this is easy ... Profit = revenue - cost

So, the
Profit = -0.00000183x^3 - 0.00029532x^2 + 30.1898x ??


K
 
no ... try again.

P(x) = R(x) - C(x)

P(x) = (-0.00000183x^3 - 0.00029532x^2 + 30.1898x) - (-0.001x^2 + 11x + 13000)

P(x) = ?
 
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