Graph y<2/3x+1 Click or tap the graph to plot a point.
1 answer:
Answer:
See below
Step-by-step explanation:
a) Create a table containing a few values of x and y
<u> x </u> <u> y </u>
-2 -⅓
-1 ⅓
0 1
1 1⅔
2 2⅓
(b) Draw the graph
Plot the points and draw a straight line through them. Make it a <em>dashed line,</em> because the line does not include the points.
Your graph should look like Fig. 1.
<em>(d) Check a point to see if it satisfies the inequality. </em>
An easy one to check is the origin, (0, 0).
0 < ⅔(0) + 1
0 < 1
The area <em>below </em>the graph satisfies the inequality.
<em>(e) Shade in the area below the graph </em>
This shows that all points in that area satisfy the inequality. The final graph should look like Figure 2.
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Answer:
Graph B
No
Inside
Step-by-step explanation:
Let, the number of apples = x and number of peaches = y.
It is given that the farmer can afford maximum of 54 acres.
Thus, x + y ≤ 54.
Also, apples require 3000 gallons of water and peaches require 800 gallons of water each day.
Since, maximum amount of water is 80,000 gallons per day,
We get, 3000x + 800y ≤ 80,000.
It is required to maximize the profit given by z = 3400x + 1600y.
Thus, the system of equations becomes,
z = 3400x + 1600y
3000x + 800y ≤ 80,000.
x + y ≤ 54.
Plotting these equations gives the following graph.
We can see that the graph obtained is equivalent to Graph B.
Further, we know that the maximum value of the objective function z = 3400x + 800y is obtained at the boundary point of the solution region.
Thus, any point inside the solution region will give a feasible solution not maximum solution.
Hence, ( 30,20 ) will not maximize the profit as it lies inside the solution region.
