Use the following information to answer questions 55-57.

Consider the set of all points (x,y) that satisfy all 3 of the conditions below:

y ≥ 0

y ≤ 2x + 4

y ≤ -x + 4

The graph of this set is △ABC and its interior, which is shown shaded in the standard(x,y) coordinate plane below. Let this set be the domain of the function P(x,y) = 4x + 3y.

55. What is the maximum value of P(x,y) when x and y satisfy the 3 conditions given?

Answer and Explanation

Your Answer is

Correct Answer is D

Explanation

The coefficients of x and y are all positive numbers. Obviously, (x, y) should be on the positive semi-axis or in the first quadrant. Take the largest edge of this area, that is, y=-x+4, then there is P(x,y)=4x+3(-x+4)=4x-3x+12=x+12. If the value of the function is to be maximized, then the value of x must be maximized, which is 4. At this point, P(x,y)=4+12=16. Therefore choose D.