Download MATH 120: Intermediate Algebra

Math 1210
Applied Optimization
1)
Maximize area: A farmer has 2400 ft of fencing and wants to fence off a rectangular field that
boarders a straight river. He needs no fence along the river. What are the dimensions of the field
that has the largest area?
2)
Maximize Cost: A cylindrical can is to be made to hold 1L of liquid. Find the dimensions of
the can that will minimize the cost of the metal to manufacture the can.
3) Distance: Find the point on the parabola y 2  2 x that is closest to the point (1, 4)
4) Area: Find the area of the largest rectangle that can be inscribed inside a semicircle of radius r.
5) Maximizing Revenue: A store has been selling 200 Blue-ray players a week at $350 each. A
market survey indicates that for each $10 rebate offered to buyers, the number of units sold will
increase by 20 a week. Find the demand function and the revenue function. How large a rebate
should the store offer to maximize its revenue.
6)
Cost: A rectangular storage container with an open top is to have a volume of 10 m3 . The length of
its base is twice the width. Material for the base costs $10 per square meter. Material for the sides
costs $6 per square meter. Find the cost of materials for the cheapest such container.
7) Unknown Numbers: Find two numbers whose difference is 100 and whose product is a
minimum.
8) Distance: What is the minimum vertical distance between the parabolas y  x 2  1 and
y  x  x2