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. complete parts (a) through (c) below.
the inequality is ( 188x + 141y leq 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 x - intercept

Set \(y = 0\) in the equation \(188x+141y=564\). Then \(188x=564\), so \(x=\frac{564}{188}=3\).

Step2: Find the y - intercept

Set \(x = 0\) in the equation \(188x + 141y=564\). Then \(141y=564\), so \(y=\frac{564}{141}=4\).

Step3: Analyze the inequality

The inequality \(188x + 141y\leq564\) represents the region below (or on) the line \(188x + 141y=564\) in the first quadrant (\(x\geq0,y\geq0\)). The line \(188x + 141y = 564\) passes through the points \((3,0)\) and \((0,4)\) and the boundary line is solid (since the inequality is \(\leq\)).

Answer:

Assuming the graph in option A has the line passing through \((3,0)\) and \((0,4)\) with the region below (or on) the line in the first quadrant, then the answer is A.