Finding the Optimum
Not what you're looking for?
The purpose of this project is to find the values of x and y that will yield the optimum (maximum or minimum) value of a system and the optimum value of a system using algebraic and graphical methods.
Follow these ten steps (see mp1.jpg) to determine the optimum value of z and the values of x and y that yield the optimum value.
The second attachment (mp1.jpg) has a similar project aimed at finding the dimensions of a picture frame that will give the largest possible interior area.
See attached file for full problem description.
Purchase this Solution
Solution Summary
The solution explains how to find the extrema (max or min) of a function z = f(x, y) in a step-by-step manner. A similar method is used in an example involving finding a maximum area for a picture frame.
Solution Preview
**See the attached file for the same text.**
Question 1: For the first problem, I'm just going to follow the steps that the problem spells out (the goal of this problem is to find a local maximum or minimum of f(x, y)). For the first two steps, I'm just making up equations.
1. z = f(x, y) = 5x2 + 2y
2. y = 3x + 5
3. Equation 2 is already solved for y, so we don't have to do any extra work here.
4. I'm going to choose x = 0.
5. y = 3(0) + 5 = 0 + 5 = 5
6. Plug x = 0 and y = 5 into equation 1:
f(x, y) = 5x2 + 2y
f(0, 5) = 5(0)2 + 2(5) = 0 + 10 = 10
z = 10
7. If you do steps 4 - 6 with many values of x, you get the following values of y and z:
x y z
-5 -10 105
-4 -7 66
-3 -4 37
-2 -1 18
-1 2 9
0 5 10
1 8 21
2 11 42
3 14 73
4 17 114
5 20 165
6 23 226
7 26 297
8 29 378
9 32 469
10 35 570
It looks like there is a minimum of z = 9 (you just look for the smallest value of z). This happens when x = -1. Let's look at values of x close to ...
Purchase this Solution
Free BrainMass Quizzes
Geometry - Real Life Application Problems
Understanding of how geometry applies to in real-world contexts
Graphs and Functions
This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.
Solving quadratic inequalities
This quiz test you on how well you are familiar with solving quadratic inequalities.
Exponential Expressions
In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.
Know Your Linear Equations
Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.