1)Sylvia has an apple orchard. One season, her 100 trees yielded 140 apples per tree. She wants to increase her production by adding more trees to the orchard. However, she knows that for every 10 additional trees she plants, she will lose 2 apples per tree (i.e., the yield per tree will decrease by 2 apples). How many trees should she have in the orchard to maximize her production of apples?
trees
2Rosalie is organizing a circus performance to raise money for a charity. She is trying to decide how much to charge for tickets. From past experience, she knows that the number of people who will attend is a linear function of the price per ticket. If she charges 5 dollars, 1160 people will attend. If she charges 7 dollars, 930 people will attend. How much should she charge per ticket to make the most money? (Round your answer to the nearest cent.)
$
3)A Norman window is a rectangle with a semicircle on top. Suppose that the perimeter of a particular Norman window is to be 16 feet. What should the rectangle's dimensions be in order to maximize the area of the window and, therefore, allow in as much light as possible? (Round your answers to two decimal places.)
width  ft 
height  ft 
4Jun has 360 meters of fencing to make a rectangular enclosure. She also wants to use some fencing to split the enclosure into two parts with a fence parallel to two of the sides. What dimensions should the enclosure have to have the maximum possible area? (Enter your answers as a commaseparated list.)
Answer in meters
5)You have $6000 with which to build a rectangular enclosure with fencing. The fencing material costs $30 per meter. You also want to have two partitions across the width of the enclosure, so that there will be three separated spaces in the enclosure. The material for the partitions costs $25 per meter. What is the maximum area you can achieve for the enclosure? (Round your answer to the nearest whole number.)
m^{2}
6)Steve likes to entertain friends at parties with "wire tricks." Suppose he takes a piece of wire 52 inches long and cuts it into two pieces. Steve takes the first piece of wire and bends it into the shape of a perfect circle. He then proceeds to bend the second piece of wire into the shape of a perfect square. What should the lengths of the wires be so that the total area of the circle and square combined is as small as possible? (Round your answers to two decimal places.)
length of wire for the circle  in 
length of wire for the square  in 
What is this combined minimal area? (Round your answer to two decimal places.)
in^{2}
7)Two particles are moving in the xyplane. They move along straight lines at constant speed. At time t, particle A's position is given by
1 
2 
and particle B's position is given by
1 
3 

particle A  (x, y) =


particle B  (x, y) =

7)
Subject  Mathematics 
Due By (Pacific Time)  07/12/2013 10:30 am 
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