Question

Find two positive real numbers whose product is a maximum. the sum of the first and three times the second is 60.

Answer 1

p = f*s
f +3s = 60

p = (60 -3s)*s = 3(20 -s)*s

This equation describes a parabola that opens downward. The roots of the equation are s=0 and s=20, so the axis of symmetry is s=(0+20)/2 = 10. That is, the vertex (maximum) will be found at s=10.

The second number is 10. The first number is 60-3*10 = 30.

The product is maximized when the first number is 30 and the second is 10.