Question: A designer uses task L to generate two outputs x1 and x2 based on the output functions x1 = 10L1 - 0.5L2 and x2= 8L2

A designer uses task L to generate two outputs x1 and x2 based on the output functions x1 = 10L1 - 0.5L2 and x2= 8L2 - 0.75L2 where Li is the work available to the domain i = 1, 2. This designer wants to maximize the value of the total output V = 4x1 + 5x2 where 4 and 5 are the global prices for x1 and x2 respectively. Assuming that the available work units are 12, find the optimal distribution of labor and its cost-effectiveness using KKT conditions.

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