Max Min Word Problems

Maximum and Minimum Word Problems 1.) The number of miles M that a certain automobile can travel on one gallon of gasoline at a speed of v mph is given by: i f M = —1v 2+ -^-v 30 2

a.) Find the speed that will be the most economical, b.) Find the largest value of M. 2.) An object is projected vertically upward from the top of a building with an initial velocity of 144 ft/sec. Its distance s(t) in feet above the ground after t seconds is given by the equation? s(r) = -16; 2 +144^ + 100 a.) Find its maximum distance above the ground? b.) Find the height of the building? c.) How many seconds will pass before it hits the ground? 3.) Flights of leaping animals typically have parabolic paths. Suppose a frog is placed on a coordinate plane at the point (0,0). The length of the leap is 9 feet and the maximum height above the ground is 3 feet. Find the equation for the path of the frog.

4.) A real estate company owns 180 efficiency apartments, which are fully occupied when the rent is $300 per month. The company estimates that for each $10 increase in rent, 5 apartments will become unoccupied. What rent should be charged so that the company will receive the maximum monthly income?

5.) A cable television firm presently serves 5000 households and charges $20 per month. A marketing survey indicates that each decrease of $1 in the monthly will result in 500 new customers. Find the price that the cable company should charge to get the maximum monthly revenue?