If a manufacturer sells x units of a certain product, his revenue R and cost C (in dollars) are given by the following equations. Use the fact that "profit = revenue - cost" to determine how many units he should sell to enjoy a profit of at least $1750.
R = 22x
C = 5000 + 7x + 0.003x2

 

P=R-C

P=22x - (5000 + 7x + 0.003x^2)

P=22x - 5000 - 7x - 0.003x^2

P= - 0.003x^2 +15x-5000 

- 0.003x^2 +15x-5000 > 1750

- 0.003x^2 +15x- 6750 > 0

 0.003x^2 -15x+ 6750 < 0

roots

{x=4500, x=500} = {x=500, x=4500}

this is a concave up parabola so it will be below 0 in the middle

 

500 < x < 4500