Question

a patient is not allowed to have more than 552 milligrams of cholesterol per day from a diet of eggs and meat. each egg provides 184 milligrams of cholesterol. each ounce of meat provides 138 milligrams of cholesterol. completes parts (a) through (c) below. the inequality is 184x + 138y ≤ 552. (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 x - intercept

Set \(y = 0\) in the equation \(184x+138y=552\). Then \(184x=552\), so \(x=\frac{552}{184}=3\).

Step2: Find y - intercept

Set \(x = 0\) in the equation \(184x + 138y=552\). Then \(138y=552\), so \(y=\frac{552}{138}=4\).

Step3: Analyze the inequality

The inequality is \(184x + 138y\leqslant552\). The boundary line \(184x + 138y=552\) is a solid line (because of \(\leqslant\)). Also, since \(x\geqslant0\) and \(y\geqslant0\), we are in the first - quadrant. We can test the origin \((0,0)\) in the inequality \(184(0)+138(0)=0\leqslant552\), so the region that contains the origin is the solution region.

Answer:

B.