Question

If a + b = 18, find the maximum value of (a - 4)(b + 1) given that a & b are positive numbers.

• A. 55
• B. 56.25
• C. 56.5
• D. 56

Answer 1

The correct option is B 56.25

Here we will not take a = b = 9 and calculate the maximum value equal to 5 $\times$ 10 = 50. The error here is that we are not finding the maximum value of a $\times$ b but (a - 4) $\times$ (b + 1).
Therefore, we need to first find the sum of (a - 4) and (b + 1).
Now (a - 4) + (b +1) = a + b - 3 = 18 - 3 = 15
So, a = b = 7.5 (for maximum value)
Therefore, the maximum value = 7.5 $\times$ 7.5 = 56.25.