Profit Function

[nycmath]

Precalculus
Michael Sullivan
Edition 10
Chapter 2, Srctiom 2.1

See attachment.

[Math Tutor]

(a) Profit is revenue minus cost, so subtract and combine like terms:

[tex]P(x) = R(x) - C(x) = 30x - (0.1x^2 + 7x + 400)[/tex]
[tex]P(x) = 30x - 0.1x^2 - 7x - 400[/tex]
[tex]P(x) = -0.1x^2 + 23x - 400[/tex]

Watch the minus sign - it distributes to all three terms of C(x).

(b) Now substitute x = 30:

[tex]P(30) = -0.1(30)^2 + 23(30) - 400[/tex]
[tex]P(30) = -0.1(900) + 690 - 400[/tex]
[tex]P(30) = -90 + 690 - 400 = 200[/tex]

(c) P(30) =\$200 means that when 30 clocks are sold, the revenue exceeds the cost by \$200, so the company makes a profit of $200.

[nycmath]

(a) Profit is revenue minus cost, so subtract and combine like terms:

[tex]P(x) = R(x) - C(x) = 30x - (0.1x^2 + 7x + 400)[/tex]
[tex]P(x) = 30x - 0.1x^2 - 7x - 400[/tex]
[tex]P(x) = -0.1x^2 + 23x - 400[/tex]

Watch the minus sign - it distributes to all three terms of C(x).

(b) Now substitute x = 30:

[tex]P(30) = -0.1(30)^2 + 23(30) - 400[/tex]
[tex]P(30) = -0.1(900) + 690 - 400[/tex]
[tex]P(30) = -90 + 690 - 400 = 200[/tex]

(c) P(30) =\$200 means that when 30 clocks are sold, the revenue exceeds the cost by \$200, so the company makes a profit of $200.

Thank you. You are very kind.