College Algebra & Trigonometry, 2018a

246 CHAPTER 4. FUNCTIONS
Exercises 4.9(b)
1) A rectangular storage container with an open top has a volume of 10 m 3 .
The length of its base is twice the width. Material for the base costs $10 per
square meter. The sides require material that costs $6 per square meter. Find the
cost of materials for the cheapest such container.
2) A poster is to contain 108 cm 2 of printed matter, with margins of 6 cm each
at the top and bottom of the page and 2 cm on each side of the page. What is the
minimum cost of the poster if it is to be made of material which costs $0.20 per
square centimeter?
3) If 1200 cm 2 of material is available to make a box with a square base and an
open top, find the largest possible volume of the box.
4) A box with a square base and open top must have a volume of 32,000 cm 3 .
Find the dimensions of the box that minimizes the amount of material used.
5) A Norman window has the shape of a semi-circle on top of a rectangle so
that the diameter of the semi-circle is the same as the width of the rectangle.
Given that the perimeter of the window should be 30 ft, find the dimensions of
the window that will admit the greatest amount of sunlight (maximize the area).
6) A rectangular box with no top is to be made from material costing $0.50 per
square foot. The width of the base is 5 ft and it will have a volume of 6 ft 3 . What