Hi good morning:

As the following is a nonlinear programming problem, I think solve it through Lagrange multipliers

but I have some problems:

The Levins' fitness sets offer an interesting application of the notion of convex sets in . A genotype of a particular species can have different "fitness", and ,

in two different environments. Assume that all genotypes of the species correspond to the points of convex set , and .

What is the genotype (the set point) that maximizes:

(These are the fittest genotypes in the environment first, the environment, secondly, and a mixed environment, respectively).

SOLUTION:

Since this is a nonlinear problem, Taking Lagrange multipliers, we:

Do:

(1)

(2)

(3)

From Equation (1)

From Equation (2)

From Equation (3)

I understand that there is now clear that replacing each variable in equations (1), (2), and (3),

To put everything in terms of .

Find and make the Hessian matrix, so it would be nice '?. This not see it, I very much appreciate if you help me finish this exercise

a greeting and thank you very much