Can you turn y=-4x+4 into a word problem

Answer 1

If price = $400, the store can't sell anything. No one buys their product

If price = zero, they "sell" or give away 100. No one wants a 101st. They can't give away more than 100.

What is the revenue maximizing price?

y=-4x+4 means P=-4x +400 = Price (you could work with 4x+4 literally, but then you get fractions of x, which is harder to make sense of for this problem)

Revenue = Price times x, quantity sold = Px = -4x^2 +400x

take the derivative and set equal to zero

R'(x) = -8x +400=0

x = 400/8 = 50 = revenue maximizing output

or graph the demand curve. revenue maximizing output is the midpoint of the demand cuve line segment from the x and y intercepts. midpoint is the point (50,1000) with P measured on the y axis, and x on the x axis.

profit maximum = -4(50)^2 +400(5) = -1000+2000 = $1,000