Matheno - Learn Well and Excel

Optimization

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.

1. Least expensive open-topped can
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?

Click to view full Calculus solution to “Least expensive can.”

2. Garden fence
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?

Click to view full Calculus solution to “Garden fence.”

3. Printed poster
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?

Click to view full Calculus solution to “Printed poster.”

Small owl logo
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 and use code “CS5OFFBTS18” (exp. 11/30/2018) to get \$5 off your first month of Chegg Study, and gain immediate access to step-by-step solutions to most textbook problems as well as answers to your specific questions from a math expert.

Open for offer details

Coupon Information
Code: CS5OFFBTS18
Promotion: \$5 off your first month’s subscription.
Disclaimer: Chegg Study users receive \$5.00 discount off the first month of a new Chegg Study subscription. Discount expires on 11/30/2018. Offer valid on a monthly subscription. Subscription can be cancelled at any time. Cannot be combined with any other offer. Valid for one-time use only. Limit one coupon per person. No cash value.

[collapse]
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.