Reference no: EM132473169
There are two divisions, the first one, when given resources x1 produces profits f1(x1) = 200α√x1, while the second one produces f2(x2) = 200β√x2. 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 of α and β, the profits to equal division of 100 between the two divisions.
2. Using the Lagrange multiplier method, solve, as a function of α and β, the problem max(x1,x2) f1(x1) + f2(x2) subject to x1 + x2 ≤ X.
3. Compare, as a function of α and β, 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) involves x1 + x2 = 100
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