Question 1128754
The price p of a certain product and the quantity sold x obey the demand equation
 p = {{{-2/3}}}x + 200 where x is greater than or equal to 0 and less than or equal to 300.
 Suppose that the cost C of producing x units is C = {{{sqrt(x)/20}}} + 800. 
Assuming that all items produced are sold, find the cost C as a function of the price p.
 Simplify your answer.
:
solve for x
{{{-2/3}}}x + 200 = p
multiply by 3
-2x + 600 = 3p
-2x = 3p - 600
multiply by -1
2x = -3p + 600
divide by 2
x = {{{-3/2}}}p + 300
we can write it
x = -1.5p + 300
:
C = {{{sqrt(x)/20}}} + 800
replace x with (-1.5p+300)
C = {{{sqrt(-1.5p+300)/20 + 800}}}