MTH 1730
Worksheet (10/16/08)
“Optimization”
(1) Find the absolute maximum and minimum values of f(x) = (x2+x)2/3on the interval
[−1,3].
(2) Find the absolute maximum and minimum values of g(x) = 3x
√4x2+ 1 on the interval
[−1,1].
(3) A liquid form of penicillin manufactured by a pharmaceutical firm is sold in bulk
at a price of $200 per unit. If the total production cost (in dollars) for xunits is
C(x) = 500,000 + 80x+.003x2and if the production capacity of the firm is at most
30,000 units in a specified time, how many units of penicillin must be manufactured
and sold in that time to maximize the profit?
(4) You have been asked to design a 1-liter can shaped like a right circular cylinder (like
a can of soda). What dimensions will use the least material? (1 liter = 1000 cm3)
(5) A farmer has 2400 ft of fencing and wants to fence off a rectangular field that borders
a straight river. He needs no fence along the river. What are the dimensions of the
field that has the largest area?
(6) The top and bottom margins of a poster are each 6 cm and the side margins are each
4 cm. If the area of the printed material on the poster is fixed at 384 cm2, find the
dimensions of the poster with the smallest area.
