There are two divisions, the first one, when given resourcesx1produces profitsf1(x1) = 200x1, while the second one producesf2(x2) = 200x2. There is a total amount X=100 of the resource that can be split in any manner between the two divisions.

1.Give, as a function ofand, the profits to equal division of 100 between the two divisions.

2.Using the Lagrange multiplier method, solve, as a function ofand, the problem max(x1,x2)

f1(x1) +f2(x2) subject tox1+x2X.

3.Compare, as a function ofand, the maximal and the equal division profits.

4.Find the price,p, for the resource at which the profit maximization problem

max(x1,x2)f1(x1) +f2(x2)p(x1+x2) involvesx1+x2= 100