A farmer wants to enclose a rectangular pen with 1,500 feet of fencing. One side of the pen will not need fencing because there is a stone wall running along that edge of the property. Find the dimensions of the pen that will have the greatest area. Make sure to identify a reasonable domain for your independent variable.

An open box (no top) is to be made by cutting congruent squares from each corner of a 12-inch by 12-inch sheet of metal and then folding up the sides. What size square should be cut from each corner to produce a box of maximum volume?

In planning a restaurant, it is estimated that a daily profit of $6 per seat will be made if the number of seats is no more than 50. If the restaurant goes beyond 50 seats, the daily profit per seat will decrease by $0.10 per seat for each seat above 50. a. Find the number of seats that will produce the maximum daily profit.

The sale of compact disks of "lesser" performers is very sensitive to price. To sell CD's, a CD manufacturer must charge = 12 q/8000 dollars per CD.

a. Find an expression for the total revenue from the sale of CD'.

b. Find the value of that leads to maximum revenue and the maximum revenue.

c. Find an expression for , the elasticity of demand, and compute the elasticity for the value of you found in part b.