3.7 Optimization Problems

3.7 Optimization Problems - & using 1st or 2nd...

Info iconThis preview shows pages 1–8. Sign up to view the full content.

View Full Document Right Arrow Icon
Optimization Problems Section 3.7
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Applications of min/max problems ® Minimum cost ® Maximum profit ® Finding the optional pkg. size ® Minimize surface area (material) given a certain volume ® Maximize volume given a certain material ® Maximize grazing area for cows given a certain amount of fencing
Background image of page 2
Problem-Solving Strategy for Min/Max Problems 1. Assign symbols to all given quantities and quantities to be determined. Draw a sketch. 2. Write a primary eqn. for the quantity to be maximized or minimized. 3. Reduce the primary eqn. to one having a single independent variable. 4. Determine the domain of the primary eqn. 5. Determine the desired maximum or minimum value by taking derivative of eqn, finding critical points, endpoints
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 4
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 6
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 8
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: & using 1st or 2nd derivative test to determine whether its a max. or min. Economics r(x) = the revenue from selling x items c(x) = the cost of producing the x items p(x) = r(x) c(x) = the profit from selling x items (or demand) = marginal revenue = marginal cost = marginal profit dr dx dc dx dp dx Maximum Profit Maximum profit (if any) occurs at a production level at which marginal revenue equals marginal cost. Minimizing Average Cost The production level (if any) at which average cost is smallest is a level at which the average cost equals the marginal cost. Joke Time Who is the mother of Minnie? Minimum What do you call 144 cockroaches? Gross...
View Full Document

Page1 / 8

3.7 Optimization Problems - & using 1st or 2nd...

This preview shows document pages 1 - 8. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online