Two-Variable Inequality 2-3 Pg paper - Example attached

Question Description

Help me study for my Algebra class. I’m stuck and don’t understand.


Read the following instructions in order to complete this assignment and review the example (attached above)  of how to complete the math required for this assignment: 

  • Read problem 46 on page 240 of Elementary and Intermediate Algebra.

Problem #46

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


  • Assign a variable to each type of rocker Ozark Furniture makes.
  • Write a linear inequality which incorporates the given information of total board feet and the board feet required for each type of rocker.
  • On scratch paper, draw a graph of the inequality so that you have this visual to go by as you discuss the graph in your writing.  A scanned copy of this graph may be attached with your essay, but is not required.
  • 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 Instructor Guidance and be concise in your reasoning. In the body of your essay, do the following:

    • Demonstrate your solution to the above problem, making sure to include all mathematical work.
    • Describe what this graph looks like. Include information about the intercepts, the type of line needed, direction of the line, and region(s) shaded to fulfill the inequality. Any details which are pertinent to know about the graph should be mentioned.
    • Evaluate the findings in this graph. Pick a point in the shaded area and give its coordinates, and then discuss what those numbers mean in terms of rockers and board feet of lumber. Pick a point outside of the shaded area and do the same thing. Pick a point right on the line and discuss the same details. Be specific.
    • Apply the linear inequality to solve the following problem: a chain furniture store faxes an order for 175 modern rocking chairs and 125 classic rocking chairs. Will Ozark Furniture be able to fill this order with the current lumber on hand? If yes, how much lumber will they have left? If no, how much more lumber would they need to fill the order? Explain your answers.
For information regarding APA samples and tutorials, visit the Ashford Writing Center, within the Learning Resources tab on the left navigation toolbar.

Unformatted Attachment Preview

Running Head: TWO-VARIABLE INEQUALITY Running head should use a shortened version of the title if the title is long! All capital letters for the title and the words Running and Head should be capitalized as well. Two-Variable Inequality (full title; centered horizontally & vertically) First Name Last Name MAT 221 Dr. XXXXXXX XXXXXXXX Date 1 TWO-VARIABLE INEQUALITY 2 Two-Variable Inequality Be sure to have a centered title on page 1 of your papers!! [The introductory paragraph must be written by each individual student and the content will vary depending on what the student decides to focus on in the general information of the topic. YOUR INTRODUCTION SHOULD CONNECT MATH CONCEPTS AND REAL-WORLD APPLICATIONS. DO NOT INCLUDE THE DIRECTIONS IN THE INTRO! The following paragraph is not an introduction to the paper but rather the beginning of the assignment.] The objective for the first part of the assignment is to write an inequality limiting the number of strip hammocks. As explained in the text, 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. (Dugopolski, 2012, p. x) (A real page number would be included if this came from the text.) To begin, the variable must be defined for clarity. The number of full-size hammocks will be represented with “f” and the number of chair-size hammocks will be represented with “c”. Since each full size hammock requires 10 yards of canvas, the expression representing the multiplication will be 10f; and, since each chair hammock requires 5 yards of canvas, 5c will be used. The total amount of canvas that can be used is limited to 2000 yards because that is all the company has available. Since all of the canvas can be used, 2000 must be included in the solution set so “less than or equal to” will be used in the inequality. As a result, the inequality demonstrating the relationship between the variables and total canvas is: 10f + 5c ≤ 2000 If f is the independent variable (on the horizontal axis) and c the dependent variable (on the vertical axis) then the inequality can be graphed the equation using the intercepts. This TWO-VARIABLE INEQUALITY 3 process involves substituting a 0 for a variable and then solving for the other using equation steps. 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 downward as it moves from left to right. The region of the graph relevant to this problem is restricted to the first quadrant, so the shaded section is from the line towards the origin and stops at the two axes. The graph cannot extend into the other quadrants because negative hammocks are impossible to create so the graph represents real-world application. To determine if orders can be filled, test points can be used to see if they fall within the relevant section of the graph. Consider the point (105, 175) on the graph. It is inside the shaded area, which means the company could fill an order of 105 full size hammocks and 175 chair hammocks. If they made up this many items they would use: 105(10) + 175(5) = 1925 yards of striped canvas and have 75 yards left over. This means the order can be filled. Consider the point (150, 125) on the graph. It is outside the shaded area which means the company could not make up enough of both kinds of hammocks to fill this order. They would run out of canvas before all of them got made. 150(10) + 125(5) = 2125 yards of canvas required. Cannot fill the order. TWO-VARIABLE INEQUALITY 4 Consider the point (75, 250). This point is right on the line and this means the company could fill this order exactly without any canvas left over. There would be no room for mistakes in this order. 75(10) + 250(5) = 2000 If someone calls and submits an order for 120 full size hammocks and 180 chair hammocks, the company would need to determine if the order could be filled. On the graph the point (120, 180) is outside of the shaded area so the company cannot make enough striped hammocks to fill this order. By substituting in the numbers for each type of hammock and evaluating it is easy to see how much short of enough canvas the company is. 120(10) + 180(5) = 1200 + 900 = 2100 yards of canvas needed. The company is 100 yards of canvas short of being able to fill this order. [This is NOT the conclusion. It is the last portion of the assignment.] [The conclusion paragraph must be written by each individual student and the content will vary depending on what the student decides to include in their summary. DO NOT INCLUDE PERSONAL NARRATIVE LIKE “I LEARNED…” OR “WE CAN DO….”. BE SURE TO SUMMARIZE WHY THE CONCEPT(S) ARE IMPORTANT AND HOW THEY CAN BE CONNECTED TO OTHER CONCEPTS.] TWO-VARIABLE INEQUALITY 5 Reference Dugopolski, M. (2012). Elementary and intermediate algebra (4th ed.). New York, NY: McGraw-Hill Publishing. Use the word ‘Reference’ or ‘References’ as the title. THERE IS NO COLON OR UNDERLINE. Textbook should ALWAYS be included in every assignment! Be sure to use appropriate indentation (hanging), font (Arial or Times New Roman), and size (12). ...
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