3.7 Optimization Problems

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

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Optimization Problems Section 3.7

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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
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

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Unformatted text preview: & using 1st or 2nd derivative test to determine whether it’s 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...
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3.7 Optimization Problems - & using 1st or 2nd...

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