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 downward as it moves from left to right. The region of the graph which is 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.
(e) Consider the point (105, 175) on my 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.
Consider the point (150, 125) on the graph. It is outside the shaded area which means the company...
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