PRECALCULUS ADVANCED
PRECALCULUS ADVANCED
WORKSHEET 2 ON OPTIMIZATION PROBLEMS
Write a function for each problem, and then use your calculator to find the answer. Draw a sketch of the function you used, and label your answer on your sketch. Give decimal answers correct to three decimal places.
1. A box with a square base and an open top must have a volume of 32 cu. cm. Find the dimensions of
the box that will minimize the amount of material used.
2. A tank with a rectangular base and rectangular sides is open at the top. It is to be constructed so that
its width is 4 meters and its volume is 36 cubic meters. If building the tank costs $10 per square
meter for the base and $5 per square meter for the sides, what is the cost of the least expensive tank?
What are its dimensions?
3. An open box is to be made from a 8.5-inch by 11-inch piece of cardboard by cutting out squares of
equal size from the four corners and bending up the sides. What size should the squares be to obtain
a box of greatest volume?
4. A cylindrical can with closed bottom and closed top is to be constructed to have a volume of one
gallon (approximately 231 cubic inches). The material used to make the bottom and top costs $0.06
per square inch, and the material used to make the curved surface costs $0.03 per square inch. Find
the radius and height of the can to minimize the total cost, and determine what that minimum cost is.
(Volume of a cylinder = [pic] and Surface Area of a closed cylinder = [pic])
Work the following on notebook paper. Find the x- and y-intercepts and the asymptotes, and sketch the graph.
5. [pic]
Intercepts: ________________________
Vert. Asymptotes: __________________
Horiz. Asymptotes: _________________
Slant Asymptotes: __________________
6. [pic]
Intercepts: ________________________
Vert. Asymptotes: __________________
Horiz. Asymptotes: _________________
Slant Asymptotes: __________________
_________________________________________________________________________________________
Do NOT use your calculator on these. Solve algebraically and check each answer. You must show your check.
7. [pic] 8. [pic]
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