Two Variable Inequality
Robin Bettasso
Mat 221
January 20, 2013

a) Let ‘c’ be the number of classic maple rocking chairs and ‘m’ be the number of classic maple rocking chairs that Ozark Furniture Company make. b) Here we have given that a classic maple rocker requires 15 board feet of maple, and a modern rocker requires 12 board feet of maple. We have ‘c’ classic maple rocker, so total maple required for classic maple rocker chair = 15c board feet. And we have ‘m’ modern maple rocker, so total maple required for classic maple rocker chair = 12m board feet. We have total maple available is 3000 board feet.

Hence we can show this condition as:
15c + 12m ≤ 3000.
This is the inequality which is showing the given situation. c) Graph for this inequality:
d) Here this is a less than and equal to inequality, so we need to take the area which is below to the line 15c + 12m = 3000 and this will be a solid line on the boundaries. The region lies between origin to x and y – intercepts. Each point which is in the first quadrant and under the shaded area is a solution for the given inequality. So, if (x, y) is a point in the shaded region then Ozark Furniture Company can obtain x number of classic and y number of modern maple rocking chairs. So, x – axis is showing number of classic maple rocking chairs and y – axis is showing the number of modern maple rocking chairs. i) Consider the point (50, 100).

This point is indicating that company is making 50 classic and 100 modern maple rocking chairs. So, c = 50 and m = 100.
So, 15c + 12m = 15(50) + 12(100) = 750 + 1200 = 1950.
Total board maple available = 3000 board feet.
Hence, total remaining maple = 3000 – 1950 = 1050 board feet. So, (50, 100) point, which is within the region showing that the company is making 50 classic and 100 modern maple rocking chairs and using 1950 board feet of maple. In this case total waste of maple is 1050 board feet. So, the company can fill the order easily. ii) Consider...

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Two-VariableInequalities
Kathleen Kent
MAT 222 Week 2 Assignment
Guillermo Alvarez
September 22, 2014
Two-VariableInequalities
This week’s assignment will show how two-variableinequalities can be used in real-world scenarios by using independent and dependent variables. This week’s assignment will use graph representations and show how the two-variableinequalities can be incorporated into several problems to show how many of each item trucks can ship without going over their weight limit.
The first problem that I will be doing is #68 on page 539 (Dugopolski, 2012). Below, the graph shows the maximum number of TVs the 18-wheeler can hold without refrigerators, and the maximum number of refrigerators the 18-wheeler can hold without TVs.
On the X-axis, the graph shows the refrigerators, and on the Y-axis, the graph shows the TVs that the 18-wheeler can carry at a time. To find the slope of the line, I will use the two points that are on the graph, (0,330) and (110,0).
The slope is m= y1 - y2 = 0 – 330 = -330 = -3, so the slope is -3.
x1 – x2 110 – 0 110
To make it easier to find how many refrigerators and how many TVs can fit in the 18-wheeler, it would be best to have a linear equation. To find the...

...TwoVariableInequalities
Melissa Hillard
MAT222: Intermediate Algebra (GSQ1331C)
Instructor Lisa Wallace
August 10, 2013
TwoVariableInequalities
For this assignment the class was asked to solve problem 68 from page 539 of our textbook Elementary and intermediate algebra (Dugopolski, 2012). Problem 68 tells the number of refrigerators and TV’s that will fit inside of an 18 wheeler truck. The class is asked to write an inequality to describe the region of the graph that is shaded in based upon these numbers. The class is then asked to solve a combination of problems to determine how many refrigerators and TV the 18 wheeler can hold at one time.
The graph shows the number of possibilities for the number of TV’s and refrigerators that will fit in an 18 wheeler at one time. The first thing I need to do is write an inequality to describe the shaded region of the graph. I will let X represent the refrigerators and Y the TV’s.
I know that my line is going from (0,330) to (110,0). The graph has a solid line rather than a dashed line meaning that points on the line itself are part of the solution.
I know the formula I need to use to write an inequality is y=mx+b
m=y2-y1/ x2-x1
This tells me what my slope is
Y=mx+b I know that b= my y intercept, which is 330. If the lines ran parallel I would...

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TwoVariableInequality
MAT 221
11 May 2012
The purpose of this week’s assignment is to determine how many maple rocking chairs the Ozark Furniture Company can make. We will also plot the inequalities of this on a graph. Here is the information and first set of problems for the text:
Maple rockers. Ozark Furniture Company can obtain at most 3000 board feet of maple lumber for making its classic and modern maple rocking chairs. A classic maple rocker requires 15 board feet of maple, and a modern rocker requires 12 board feet of maple. Write an inequality that limits the possible number of maple rockers of each type that can be made, and graph the inequality in the first quadrant.
To determine how many classic and modern rockers can be made, we simply just divide 3000 (board feet) by how many board feet are required for the particular rocker. Here is how that looks:
3000 ÷ 15 = 250 classic rockers (C)
3000 ÷ 12 = 200 modern rockers (R)
On the next page, this inequality is graphed, classic rockers is shown on the Y axis, modern rockers on the X axis. The slope is , or simplified: .
Part two of the assignment asks if Ozark Furniture will be able to fulfill an order by a retail furniture chain. They requested 175 modern rockers and 125 classic rockers. Will there be enough maple and if so, how much. If...

...TWO-VARIABLEINEQUALITY
MAT 221
Joseph Oslakovic
February 16, 2014
TWO-VARIABLEINEQUALITY
This week we are learning about two-variableinequalities as they pertain to algebraic expressions. The inequality can be graphed to show the values included in and excluded from a given range of numbers. Solving forinequalities such as these is a critical skill in many trades which can save or cost a company a lot of time and money.
Ozark Furniture Company can obtain at most 3000 board feet of maple lumber for making its classic and modern maple rocking chairs. A classic maple rocker requires 15 board feet of maple, and a modern rocker requires 12 board feet of maple. Write an inequality that limits the possible number of maple rockers of each type that can be made, and graph the inequality in the first quadrant.
First I must assign a variable to each type of rocker Ozark Furniture makes.
Let c = the number of classic rockers
Let m = the number of modern rockers
It takes 15 board feet of lumber for each classic rocker so I will use 15c in my equation. Likewise, I will use 12m for the 12 board feet of lumber in the modern rocker. The maximum amount of lumber Ozark can obtain is 3000 board feet. Therefore, my equation will look like this:
15c +...

...Inequalities are equations that can be used to determine not just what something could equal but what something cannot equal. It tells us what the relative size is of two values and if they are big or small, too much or not enough. Inequalities could make it easier to determine how much someone might need of something in order to make a certain amount of something, while also determining how much more might be needed or how much be left. For example, if someone wanted to make cupcakes and flat cakes, they would need a specific amount of flour for each cake and cupcake. However, if they only have 12 cups of flour and cupcakes take one cup while cakes take two cups of flour an inequality would be needed to determine if there is enough flour to make 30 cupcakes and 2 flat cakes. The inequality would then be able to determine whether or not there was enough flour and if not how much more would be needed.
There is a company called Ozark Furniture that specializes in making rocking chairs. They make classical and modern rocking chairs, both of which require the same type of lumber, maple; therefore, it is important to know how many of each chair they can make with the amount of lumber at one time is 3000 board feet. However, how many classical and modernized rocking chairs are they able to make from that lumber? If they made an inequality, they could determine how and if...

...2-VariableInequality
Here is an example of a problem very similar to the one in the Week Three Assignment:
Catskills Hammock Company can obtain at most 2000 yards of striped canvas for making its full size and chair size hammocks. A full size hammock requires 10 yards of canvas and the chair size requires 5 yards of canvas. Write an inequality that limits the number of striped hammocks of each type which can be made.
(b) First I must define what variables I will be using in my inequality.
Let f = the number of full size hammocks
Let c = the number of chair size hammocks
Since each full size hammock requires 10 yards of canvas I will use 10f, and since each chair hammock requires 5 yards of canvas I will use 5c. The total amount of canvas which can be used is limited to 2000 yards because that is all they can get. Together my inequality will look like this:
10f + 5c ≤ 2000
(d) If we call f the independent variable (on the horizontal axis) and c the dependent variable (on the vertical axis) then we can graph the equation using the intercepts.
The f-intercept is found when c = 0:
10f ≤ 2000
f ≤ 200 The f-intercept is (200, 0).
The c-intercept is found when f = 0:
5c ≤ 2000
c ≤ 400 The c-intercept is (0, 400).
Because this is a “less than or equal to” inequality the line will be solid, sloping...

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This work MAT 222 Week 2 Assignment TwoVariableInequalities includes 2 parts: 1. Two-variableinequalities 2. Application of the given situation to two scenarios
General Questions - General General Questions
Two-VariableInequalities
Read the following instructions in order to complete this assignment:
Solve problem 68 on page 539 of Elementary and Intermediate Algebra, and make sure to study the given graph. For the purposes of the assignment, it would be helpful to copy the graph onto your own scratch paper.
Write a two to three page paper that is formatted in APA style and according to the Math Writing Guide . Format your math work as shown in the example and be concise in your reasoning. In the body of your essay, please make sure to include:
An answer to the three questions asked about given real-world situation.
An application of the given situation to the following two scenarios:
The Burbank Buy More store is going to make an order which will include at most 60 refrigerators. What is the maximum number of TVs which could also be delivered on the same 18-wheeler? Describe the restrictions this would add to the existing graph.
The next day, the Burbank Buy More decides they will have a television sale so they change their order to include at least 200 TVs. What...

...TwoVariableInequality
Katherine Courtney
MAT221
Phil Le
August 25, 2013
Inequalities are equations that can be used to determine not just what something could equal but what something cannot equal. It tells us what the relative size is of two values and if they are big or small, too much or not enough. Inequalities could make it easier to determine how much someone might need of something in order to make a certain amount of something, while also determining how much more might be needed or how much would be left. If a person wanted to make cupcakes and flat cakes, they would need a specific amount of flour for each cake and cupcake. However, if they only have 12 cups of flour and cup cakes take one cup while cakes take two cups of flour an inequality would be needed to determine if there is enough flour to make 30 cupcakes and 2 flat cakes. The inequality would then be able to determine whether or not there was enough flour and if not how much more would be needed.
There is a company called Ozark Furniture, that specializes in making rocking chairs. They make classical and modern rocking chairs, both of which require the same type of lumber, maple, therefore it is important to know how many of each chair they can make with the amount of lumber they already have. Ozark uses 15 board feet of maple...