Show that the sum of two concave functions is concave. is the product of two concave functions also concave?

1.

Let f and g concave functions. Then for a in (0,1), and

Now,

This shows that the function f+g is concave.

2. Let f and g concave functions.

This shows that the product of two concave functions isn't concave.

answer: evaluate the objective function at each vertex to determine which - and -values, if any, maximize or minimize the function. example: find the minimum value and maximum value of the objective function f ( x , y ) = 4 x + 5 y , subject to the following constraints

fist on the left goes with the third on the right. second on the left goes with the fourth on the right. third on the left goes with the second on the right. the fourth on the left goes with first on the right