Find the two number x and y, that give the maximum possible product x·y.

Question

The sum of one number, x, and 5 times another number, y, is 240. Find the two number x and y, that give the maximum possible product x·y.

Answer 1

x + 5y = 240

x = 240 - 5y

x*y = (240 - 5y)y =

240y - 5y^2 = f(y)

f'(y) = 240 - 10y

f'(y) = 0 when y = 24

which forces x = 240 = 24*5 = 240 - 120 = 120

the max product is 24*120 = 2880