Optimization Problems A manufacturer wants to design an

Optimization Problems ¶A manufacturer wants to design an open box having a square base and surface area of ____ square inches. What dimensions will produce the maximum volume of the box?

The Procedure ¶Assign symbols to all given quantities. When feasible, ______. ËWrite a ________ for the quantity that is to be maximized (or minimized). ÌReduce the primary equation to one having a single independent variable. This may involve the use of __________relating to the independent variables in the primary equation.

The Procedure ÍDetermine the _____ of the primary equation for the context of the problem. ÎFind the ______ using techniques from calculus previously studied.

Optimization Problems ·Find the points on the 2 graph y = 4 - x that are closest to the point _____.

Mindjog 1/7/09 z. The graph below is the derivative of f. At what interval(s) if f increasing? (-2, 0) (0, -3)

Objective: S. W. B. A. T. zuse calculus in order to solve optimization problems.

Optimization z. What is it? z. Finding the maximum or minimum values to solve a problem. This could be the largest profit, smallest cost, least time, greatest voltage, etc.

Optimization Problems ¶A manufacturer wants to design an open box having a square base and surface area of 108 square inches. What dimensions will produce the maximum volume of the box?

The Procedure ¶Assign symbols to all given quantities. When feasible, make a sketch. ËWrite a primary equation for the quantity that is to be optimized (maximized or minimized). ÌReduce the primary equation to one having a single independent variable. This may involve the use of secondary equations relating to the independent variables in the primary equation.

The Procedure ÍDetermine the feasible domain of the primary equation for the context of the problem. ÎFind the optimal values using techniques from calculus previously studied.

Optimization Problems ·Find the points on the 2 graph y = 4 – x that are closest to the point (0, 2).

Practice Problems z. Page 218 - 220 z#19, 23, 29

Homework z. Page 218 -220 z#’s 11, 16, 22, 31

2. 9 Calculus Drill 11/12/03 z. Two posts, 12 ft high and the other 28 ft high, stand 30 feet apart. They are to be stayed by two wires, attached to a single stake, running from ground level to the top of each post. Where should the stake be placed to use the least amount of wire.