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A. [This problem is based on Homework 1, Problem C and Homework 5, Problems A, G, H, and I.] A company has three production facilities that use input to produce output according to the pro- duction functions q = f1(m1) = 6,/a:1, q = f2(a:2) = 8,/a:2, and q = f3(:cs) = 2x/11 - 1:3. It can allocate a total amount of input, X, to the three production facilities as it pleases. The input is purchased in a competitive market at price w. 1. Using the Lagrangean method, show that the production func- tion, F{X) = maxmmma [f1(:131) + 13032) + f3(a:3)] subject to :61 + $2 + :33 g X is equal to 12%. [Be sure to write out the Lagrangean function and the FOCs that you are solving.]