December 08, 2014
6-2
Applications of the
Extrema
Example 1
Of all numbers whose sum is 68, find the two that have the maximum
product. That is, maximize Q = xy where x + y = 68.
Example 2
If the price charged for a candy bar is p(x) cents, then x thousand candy
bars will be sold in a certain city where
a) Find an expression for the total revenue from the sale of x thousand
candy bars.
b) Find the value of x that leads to the maximum revenue.
c) Find the maximum revenue.
Example 3
A rectangular plot of farmland will be bounded on one side by a river and
on the other three sides by a single-strand electric fence. With 2200m of
wire at your disposal, what is the largest area you can enclose and what
are its dimensions?
Example 4
Example 5
A fence must be built to enclose a rectangular area of 20,000 ft2.
Fencing material costs $2 per foot for the two sides facing north and
south and $4 per foot for the other two sides. Find the cost of the
least expensive fence.
A 1372 ft3 tank with a square base and open top is to be constructed
of sheet steel of a given thickness. Find the dimensions of the tank
with minimum weight.
December 08, 2014
Example 6
Example 7
A local club is arranging a charter flight to Hawaii. The cost of the
trip is $540 each for the 84 passengers, with a refund of $5 per
passenger for each passenger in excess of 84.
a) Find the number of passengers that will maximize the revenue
received from the flight.
b) Find the maximum revenue.
A candy box is made from a piece of cardboard measuring 35 by 19
inches. Squares of equal size will be cut out of each corner. The
sides will then be folded up to form a rectangular box. What size
square should be cut from each corner to obtain maximum volume?
Example 8
A disease has hit a city. The percentage of the population infected t
days after the disease arrives is approximated by
After how many days is the percentage of infected people a
maximum? What is the maximum percent of the population
infected?
Example 9
Johnny is designing a rectangular poster to contain 36in2 of printing
with a 2-in margin at the top and bottom and a 2-in margin at each
side. What overall dimensions will minimize the amount of paper
used?