Read the following instructions in order to complete this assignment and review the example of how to complete the math required for this assignment:
•Read problem 46 on page 240 of Elementary and Intermediate Algebra.

?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.

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 ya
rds 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 hamm
ock requires 10 yards of canvas, the expressio
n 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 c
anvas 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
graph
ed
the equation using the intercepts.
This
Running
Head
:
TWO
–
VARIABLE INEQ
UALI
TY
3
process involves substituting a 0 for a variable and t
hen 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 e
qual 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 tw
o 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
relevan
t 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 t
his 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.
Running
Head
:
TWO
–
VARIABLE INEQ
UALI
TY
4
Consider the point (75, 250). This point is right on the line and this means the company
could fill this order ex
actly 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 a
nd 180 chair
hammocks, the company would need to determine if the order could b
e 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 enou
gh 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 para
graph must be written by each individual student and the content will vary
depending on what the student decides to include in their summary.