1- A walnut grower estimates from past records that if 20 trees are planted per acre, then each tree will average 60 pounds of nuts per year. If, for each additional tree planted per acre, the average yield per tree drops 2 pounds, then how many trees should be planted to maximize the yield per acre? What is the maximum yield?
1- A walnut grower estimates from past records that if 20 trees are planted per acre, then
each tree will average 60 pounds of nuts per year. If, for each additional tree planted per
acre, the average yield per tree drops 2 pounds, then how many trees should be planted to
maximize the yield per acre? What is the maximum yield?
2- A multimedia company anticipates that there will be a demand for 20,000 copies of a
certain DVD during the next year. It costs the company $0.40 to store a DVD for one
year. Each time it must make additional DVDs, it costs $250 to set up the equipment.
How many DVDs should the company make during each production run to minimize its
total storage and setup costs?
3- Suppose $5,000 is invested at an annual interest rate of 7%. Compute the balance after
10 years if the interest is compounded:
a. Annually
b. Quarterly
c. Monthly
d. Continuously
4- Calculate the second derivative of the function y = f (x) defined by the equation
x3 + y3 +3xy + 3y2 + 6x + 6y =0 at the point x = 1
5- An article will be written on a 24 cm2 part of a paper. Since 1.5 cm from the top and
bottom and 1 cm from the right and left will be left blank, how many cm2 should the area
of this paper be at least?
6- Follow the graphing strategy and analyze the function f(x)= 3x5 -10x3 State all the
pertinent information and sketch the graph of f.
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