a store sells a certain type of bracelet. the number of bracelets sold in a month is molded by the expression -2/3+50, where x is the orice of each brcaelet.

Question

There are part a which asks: write an equation to model the monthly revenue

there is a part b which asks: at what price should the store sell the bracelet so the monthly revenue is 900$?

and part c apwhich also asks: are there any extraneous solutions?

Answer 1

generally the demand curve for in linear form would be Q=aP + b

so that as price rises, quantity demanded decreases, an inverse relationship

so odds are you meant to write

Q = -(2/3)x + 50

if so, then R= Revenue = Qx = R(x) = -(2/3)x^2 + 50x

find max R by taking the derivative and setting it equal to zero

R' = -(4/3)x + 50 = 0

4x/3 = 50

x = (3/4)50 = 75/2 = 37.5 = $37.50 per bracelet to maximize revenue

plug that into R(x) = R(37.5) = -(2/3)x^2 + 50x = -(2/3)(37.5)^2 + 50(37.5) = $937.50 = max revenue