Suppose a patient is not allowed to have more than 330 milligrams of cholesterol per day from a diet of eggs and meat. Each egg provides 165 milligrams of cholesterol and each ounce of meat provides 110 milligrams of cholesterol. Thus, 165x+110y where x less than or equal to 330 is the number of eggs and y the number of ounces of meat. Furthermore, the patient must have at least 165 milligrams of cholesterol from the diet. Graph the system of inequalities in the first quadrant.
To graph the system of inequalities, we first need to identify the vertices of the feasible region.
Let's consider the first inequality: 165x + 110y ≤ 330.
We can rewrite this inequality as: 165x + 110y - 330 ≤ 0.
To find the x-intercept, we set y = 0 and solve for x:
165x + 0 - 330 = 0
165x = 330
x = 2
To find the y-intercept, we set x = 0 and solve for y:
0 + 110y - 330 = 0
110y = 330
y = 3
So the x-intercept is (2, 0) and the y-intercept is (0, 3).
Now let's consider the second inequality: x ≥ 0 and y ≥ 0.
This means the feasible region is in the first quadrant, above the x-axis and to the right of the y-axis.
So, we have the following vertices: (2, 0), (0, 3), (0, 0)
And the feasible region is the triangular region formed by these vertices.
To plot the graph, we label the x-axis as the number of eggs (x) and the y-axis as the number of ounces of meat (y). Then we plot the points (2, 0), (0, 3), and (0, 0) and connect them to form the triangular region.