If a + b + c + d = 2, then the maximum value of (1 + a)(1 + b)(1 + c)(1 + d) is:

Answer: Option B

$$\begin{array}{rl}& a+b+c+d=2\\ & \text{Let }a=b=c=d=\frac{1}{2}\\ & \text{satisfy the above}\\ & \text{so, }\left(1+a\right)\left(1+b\right)\left(1+c\right)\left(1+d\right)\\ & =\left(1+\frac{1}{2}\right)\left(1+\frac{1}{2}\right)\left(1+\frac{1}{2}\right)\left(1+\frac{1}{2}\right)\\ & =\frac{3}{2}\times \frac{3}{2}\times \frac{3}{2}\times \frac{3}{2}\\ & =\frac{81}{16}\end{array}$$