functions: company sells x units at profit P(X)=20X-X^2

[SONCEE]

A company sell x units of a product whose profit is given by the function P(X)=20X-X^2

A) how many units should the business sell in order to maximize profits = 10

B)How much is the maximum profit = 300

C) What is the maximum number of units the business can sell to make a profit

p(x)=-x^2+20x

-B
x= 2A

X= -20 = 10 P(10) = -10^2+ 20(10) = P(10)= 100 + 200 = 300
2(-1)

Can anyone help me get the answer to C and check my answers please

 

[wjm11]

Re: function problem

A company sell x units of a product whose profit is given by the function P(X)=20X-X^2

A) how many units should the business sell in order to maximize profits = 10

B)How much is the maximum profit = 300

C) What is the maximum number of units the business can sell to make a profit

A) is correct.

B) has a math error:

P(10) = 20(10) - 10^2 = 200 - 100 = 100

For C), set P(x) = 0 and solve for x. Graphically, you have an inverted parabola. When it passes below the x axis, you're in negative territory: the company is taking a loss. The x axis is the break-even point. Make sense?

 

[SONCEE]

Re: function problem

thank you