C As A Function of p

[mathdad]

Production Cost The price p, in dollars, of a certain product and the quantity x sold obey the demand equation P=-1/4x+100, 0 ≤ x ≤ 400. Suppose that the cost C, in dollars, of producing x units is C = sqrt{x}/25+600. Assuming that all items produced are sold, express the cost C as a function of the price p.

Solution:

p = -1/4x+100

(p - 100) = (-1/4)x

(p - 100)/(-1/4) = x

-4p + 400 = x

C(p) = [sqrt{-4p + 400)/25] + 600

Yes?

 

[MarkFL]

After this line:

(p - 100)/(-1/4) = x

I would write:

x = 4(100 - p)

So that:

[MATH]C(p)=\frac{2\sqrt{100-p}}{25}+600[/MATH]
In conclusion, this line has a typo:

-4p + 400 = p

It is obvious you meant for "x" to be on the RHS. Your final result is correct, but can be simplified by factoring the square from the radicand.

 

[mathdad]

After this line:

(p - 100)/(-1/4) = x

I would write:

x = 4(100 - p)

So that:

[MATH]C(p)=\frac{2\sqrt{100-p}}{25}+600[/MATH]
In conclusion, this line has a typo:

-4p + 400 = p

It is obvious you meant for "x" to be on the RHS. Your final result is correct, but can be simplified by factoring the square from the radicand.

Thanks. I updated the typo. Another one for the files. More math later. Not working today.