Find two positive numbers such that the sum of the first and twice the second is 56 and whose product is a maximum.
B) 28 and 14

Question

Quizplus · Accepted Answer

Let the two numbers be x and y. Then we have:

x + 2y = 56 (since the sum of the first and twice the second is 56)

xy = x(56-2y) = 56x - 2x^2

To find the maximum value of xy, we can use the formula for the vertex of a parabola:

x = -b/2a, where ax^2 + bx + c represents the quadratic function.

In this case, a = -2, b = 56, and c = 0, so:

x = -56/(2*-2) = 14

Substituting this value back into the first equation, we can solve for y:

14 + 2y = 56

2y = 42

y = 21

Therefore, the two numbers are 14 and 21, and their product is 14*21 = 294, which is the maximum possible product.

Find Two Positive Numbers Such That the Sum of the First