Solution for QID #28247: The profit function for a certain commodity isP(x) =180x&min | StudyHelpMe

The profit function for a certain commodity is P(x) = 180x − x2 − 2000.  Find the level of production that yields maximum profit, and find the maximum profit. x= p=   A supply function and a demand function are given. Supply: p= 1/3q^2+8 Demand: p= 53-5q-3q^2 Algebraically determine the market equilibrium point.     If total costs are C(x) = 3500 + 3380x  and total revenues are R(x) = 3500x − x2,  find the break-even points.   If, in a monopoly market, the demand function for a product is p = 160 − 0.80x  and the revenue function is R = px,  where x is the number of units sold and p is the price per unit, what price will maximize revenue?   The monthly profit from the sale of x units of a product is P = 60x − 0.04x2 − 14,000  dollars. a. What level of production maximizes profit? b. What is the maximum possible profit?   Two projectiles are shot into the air from the same location. The paths of the projectiles are parabolas and are given by (a) y = −0.0013x^2 + x + 16    and (b) y = −x^2 / 81 +4/3x+16 where x is the horizontal distance and y is the vertical distance, both in feet. Determine which projectile goes higher by locating the vertex of each parabola. (a)    y = −0.0013x^2 + x + 16 (b)    y = −x^2/81 + 4/3x + 16   What is the projectile that goes highest and how many feet higher does it go than the other projectile?