Ch3/4 Lesson 8b Problem Solving Involving Max and Min

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Ch3/4 Lesson 8b Problem Solving Involving Max and Min i) Maximum area ii) Minimum for sums of two squares © Copyright all rights reserved to Homework depot: www.BCMath.ca

Max /Min Problems In this section we will look at word problems that involves finding the Maximum or Minimum of a situation Ie: Building a rectangular barn with the biggest area possible but restricting the perimeter The smallest rectangle that you can make inside a right triangle Given two numbers with some restrictions, then finding the smallest possible product of these two numbers In general, you will have two equations, plug one equation into the other to make a quadratic function The quadratic function will be used the find the maximum or minimum of something: area, product, Use CTS or XAV or -b/2a to find the vertex

II) Common terms: Sum  Add , sum of two numbers is 10 Difference  Subtract, the diff. of two numbers is 8 Product  Multiply, the product of two numbers is a maximum value Sum of their squares  Square the numbers & then add them, the sum of their squares is a minimum Perimeter  length of all the edges, the perimeter of a rectangle is 200m © Copyright all rights reserved to Homework depot: www.BCMath.ca

Ex: The sum of two numbers is 80. Their product is a maximum Ex: The sum of two numbers is 80. Their product is a maximum. Write an equation for the product and then find the numbers The sum is 80 The “product” is a maximum 2. Method Xavier Substitute the first eq. into the second one. Find the vertex because the vertex is the maximum The maximum is 1600, when x = 40 and y = 40

Ex: The difference of two numbers is 10 Ex: The difference of two numbers is 10. The sum of their squares is a minimum. Find the numbers The difference is 10 The sum of their squares is a minimum Substitute the first equation into the second one. Complete the square The minimum occurs when x = –5 The other number is: Sum of the squares is: © Copyright all rights reserved to Homework depot: www.BCMath.ca

Isolate one variable Complete the square Ex#3) A farmer wants to build a rectangular barn using 100 meters of fencing for his cows and chickens. However, he needs to separate the two groups of animals and needs to make the largest possible area. Determine the dimensions for the barn. Isolate one variable Complete the square © Copyright all rights reserved to Homework depot: www.BCMath.ca

practice: Suppose you have 400m of fencing to build a rectangular garden as illustrated below, what are the dimensions of the largest possible area?