Question

If a, b, c and d are four positive numbers such that a + b + c + d = 4, then what is the maximum value of (a + 1)(b + 1) (c + 1)(d + 1) ?

• A. 32
• B. 8
• C. 16
• D. 81

Answer 1

The correct option is C 16

If a + b + c + d is constant, then the product abcd is maximum when a = b = c = d.
$\therefore (a+1)=(b+1)=(c+1)=(d+1)$
Given that $a+b+c+d=4$
$\therefore$(a + 1) + (b + 1) + (c + 1) + (d + 1) = 8
$\therefore 4(a+1)=8$
$\Rightarrow (a+1)=(b+1)=(c+1)=(d+1)=2$
$\therefore$ Maximum value $=2\times 2\times 2\times 2=16$