Find the maximum profit given by the revenue and cost functions​ below, where x is in thousands of units and​ R(x) and​ C(x) are in thousands of dollars.   R(x)=107x-x^2 C(x)=1/3x^3-6x^2+63x+32   A 400 thousand dolars   B. 464 thousand dollars   C. 256 thousand dollar   D 688 thousand dollars.

The demand for memory sticks is given by the function Qd=97.8-5p while its supply is given by Qs = 23e^(0.04p)+4 where the price p in dollars and Qs is the number of memory sticks produced and Qd is the number of sticks sold. At a price of $10 is there a surplus or shortage of how many memory sticks?

The number of thousand mp3 players produced per month by a certain manufacturer t months after the start of the year 2004 can be described by the function f(t)=0.2t^2 + 3t + 3 As they sell more players, the company's profit increases both because they are selling more players and because economies of scale mean they can produce each player more cheaply. The manufacturer's total profit (in thousands of dollars) when x thousand mp3 players are made is given by the function g(x)=0.01x^2 +4x +20 We assume that the company sells all of the mp3 players that it produces. Calculate the rate at which the sales of mp3 players increases (in thousands of players per month) in terms of t.   Rate of increase :  .4t +3 thousand players per month. Calculate the rate at which the manufacturer's profit increases (in thousands of dollars per thousand mp3 players) in terms of x.   Rate of increase :  .02x +4 thousand dollars per thousand mp3 players. ?? Calculate the rate at which the manufacturer's…

suppose you and your friends create a catapult and launch a water balloon with it. A. the height of the water balloon in feet t seconds after launch is given by f(t) =96t-16t^2. how long will the water balloon be in the air? (here we assume the water balloon is on the ground when the height is 0 ft.) B. viewing a graph of this function below, estimate the maximum height the water balloon achieves. (image of graph below) C. recalling that the function of the height of the water balloon (in feet) is f(t) =96t-16t^2 , use your knowledge about quadratic function to determine the actual height the water balloon achieves.