a company makes and sells sailboats. The company's cost function in thousands of dollars is C(x)=2x+20, and the revenue function in thousands of dollars is R(x)=4x, where x is the number of sailboats. Find and simplify the profit function, P(x). How many boats must be sold for the company to break even ( that is, for the profit to be zero)?
P = R - C
P = 4 x - 2 x - 20
P = 2 x - 20
for 0 profit, x = 10
P = R-C = 4x - (2x+20) = 2x-20
When P=0, x=10
Thank you so much
To find the profit function, you need to subtract the cost (C(x)) from the revenue (R(x)).
The profit function, P(x), is given by:
P(x) = R(x) - C(x)
Substituting the given revenue and cost functions:
P(x) = 4x - (2x + 20)
P(x) = 4x - 2x - 20
P(x) = 2x - 20
To find the number of boats required to break even (where profit is zero), we need to set the profit function equal to zero and solve for x:
0 = 2x - 20
Rearranging the equation:
2x = 20
x = 10
Therefore, the company must sell 10 boats to break even (where profit is zero).