Find two positive numbers A and B

Question

Find two positive numbers A and B (with A ≤ B) whose sum is 76 and whose product is maximized.

 

A=_______

 

B=_______

Answer 1

A + B = 76

 

A = 76 - B

 

AB = (76 - B)B = 76B - B² = f(B)

 

f'(B) = 0 = 76 - 2B ⇒ B = 76/2 = 38

 

A = 76 - B = 76 - 38 = 38

 

A = B = 38