Optimization: Problems and Solutions
We will solve every Calculus Optimization problem using the same Problem Solving Strategy time and again. You can see an overview of that strategy here (link will open in a new tab).
We use that strategy to solve the problems below.
An open-topped cylindrical can must contain V cm$^3$ of liquid. (A typical can of soda, for example, has V = 355 cm$^3$.) What dimensions will minimize the cost of metal to construct the can?
Sam wants to build a garden fence to protect a rectangular 400 square-foot planting area. His next-door neighbor agrees to pay for half of the fence that borders her property; Sam will pay the rest of the cost. What are the dimensions of the planting area that will minimize Sam’s cost to build the fence?
What are the dimensions of the poster with the smallest total area?
A poster must have a printed area of 320 cm$^2$. It will have top and bottom margins that are 5 cm each, and side margins that are 4 cm. What are the dimensions of the poster with the smallest total area?
Want access to all of our Calculus problems and solutions? Buy full access now — it’s quick and easy!
Do you need immediate help with a particular textbook problem?
Head over to our partners at Chegg Study and gain (1) immediate access to step-by-step solutions to most textbook problems, probably including yours; (2) answers from a math expert about specific questions you have; AND (3) 30 minutes of free online tutoring. Please visit Chegg Study now.
If you use Chegg Study, we’d greatly appreciate hearing your super-quick feedback about your experience to make sure you’re getting the help you need.