1. Ch3/4 Lesson 8b Problem Solving Involving Max and Min
i) Maximum area
ii) Minimum for sums of two squares
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2. 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

3. 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
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4. 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

5. 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:
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6. 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
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7. practice: Suppose you have 400m of fencing to build a rectangular garden as illustrated below, what are the dimensions of the largest possible area?