Question

a patient is not allowed to have more than 564 milligrams of cholesterol per day from a diet of eggs and meat. each egg provides 188 milligrams of cholesterol. each ounce of meat provides 141 milligrams of cholesterol. completes parts (a) through (c) below
the inequality is 188x + 141y ≤ 564.
(use integers or decimals for any numbers in the expression.)
b. graph the inequality. because x and y must be positive, limit the graph to quadrant i only. choose the correct graph below

Explanation:

Step1: Find the intercepts

For \(x\)-intercept (\(y = 0\)):

$$
LATEXBLOCK0
$$

For \(y\)-intercept (\(x = 0\)):

$$
LATEXBLOCK1
$$

The line \(188x + 141y=564\) passes through the points \((3,0)\) and \((0,4)\)

Step2: Analyze the inequality \(188x + 141y\leq564\)

Since \(x\geq0\) and \(y\geq0\) (quadrant I), the region \(188x + 141y\leq564\) is the set of points \((x,y)\) in the first - quadrant that lie on or below the line \(188x + 141y = 564\)

Answer:

The graph should have the line connecting \((3,0)\) and \((0,4)\) with the region below (and including) the line in the first quadrant. If we assume the options:

• Option A: If the \(x\)-intercept is \(3\) and \(y\)-intercept is \(4\) and the region is below the line in the first quadrant (smaller values of \(x\) and \(y\) as it is a "less - than - or - equal - to" inequality for positive \(x\) and \(y\)), then the correct graph is likely Option A (assuming the other options have incorrect intercepts or shading directions).