Optimization. Objective  To solve applications of optimization problems  TS: Making decisions after reflection and review.

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Presentation transcript:

Optimization

Objective  To solve applications of optimization problems  TS: Making decisions after reflection and review

Optimization  Optimization is the procedure used to make a design as effective as possible.

Number Problem  The product of two positive numbers is 288. Minimize the sum of twice the first number plus the second number. Primary Equation Secondary Equation

Number Problem Primary Equation Solve for y Substitute y into Primary Equation Simplify Differentiate

und This is Not Positive! Find critical points Test 0 0 Min

Number Problem Numbers:

The Fence Problem  A farmer has 100 ft of fencing to enclose a rectangular field. The field will have one side along his farmhouse, and thus needs to be fenced on only three sides. What are the dimensions of the rectangle that will maximize the area? Maybe it looks like this… or this… or this.

The Fence Problem  A farmer has 100 ft of fencing to enclose a rectangular field. The field will have one side along his farmhouse, and thus needs to be fenced on only three sides. What are the dimensions of the rectangle that will maximize the area? w w l

The Fence Problem Primary Equation Secondary Equation Solve for l Substitute l into Primary Equation Simplify Differentiate

The Fence Problem Find critical points MAX Test 0

The Fence Problem Dimensions:

The Box Problem  An open box is to be constructed from a piece of cardboard which is 16” by 13”, by cutting out a square from each of the four corners and bending up the sides. What size square should be removed from each corner in order to create a box that maximizes volume?

The Box Problem  An open box is to be constructed from a piece of cardboard which is 16” by 13”, by cutting out a square from each of the four corners and bending up the sides. What size square should be removed from each corner in order to create a box that maximizes volume?

The Box Problem h hh h h l w h hh h h hh h h hh h

Primary Equation Secondary Equations Substitute l and w into Primary Equation Simplify Differentiate

The Box Problem Find critical points Test Quadratic Formula 0 0 MAX MIN Dimensions of square: