Question

a patient is not allowed to have more than 624 milligrams of cholesterol per day from a diet of eggs and meat. each egg provides 208 milligrams of cholesterol. each ounce of meat provides 156 milligrams of cholesterol. completes parts (a) through (c) below. the inequality is 208x + 156y ≤ 624. (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. a. b. c. d.

Explanation:

Step1: Find the intercepts

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

$$
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$$

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

$$
LATEXBLOCK1
$$

The line \(208x + 156y=624\) passes through the points \((3,0)\) and \((0,4)\).

Step2: Determine the region

Since the inequality is \(208x + 156y\leq624\) (non - negative \(x\) and \(y\) as \(x\) represents number of eggs and \(y\) represents ounces of meat, so \(x\geq0,y\geq0\)), we test the origin \((0,0)\):

$$208\times0+156\times0=0\leq624$$

The region that contains the origin and is in the first quadrant (\(x\geq0,y\geq0\)) is the solution region.

Answer:

The correct graph is the one where the line passes through \((3,0)\) and \((0,4)\) and the region below (and including) the line in the first quadrant. Without seeing the exact details of the options A - D, but based on the intercepts \((3,0)\) and \((0,4)\) and the fact that the origin \((0,0)\) is in the solution set (shaded region), if we assume standard graphing:
If option A has the line \(208x + 156y = 624\) with intercepts \((3,0)\) and \((0,4)\) and the region below (including the line) in the first quadrant, then A is correct. But if we assume that the line is solid (because the inequality is \(\leq\)) and the region is bounded by \(x = 0,y = 0\) and the line \(208x+156y=624\) in the first quadrant.