Production function of a company is given by f(X,y) = I; + J; wherex is labor and y is capital. Cost of labor is 2 currency units, while the cost of
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 Unconstrained Optimization, Lagrange problem, Least Squares

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Production function of a company is given by f(X,y) = «I; + J; wherex is labor and y is capital. Cost of labor is 2 currency units, while the cost of capital is 1 currency unit. What are the minimal cost to produce 10 units of the product? What is the change in the costs, if the production volume would increase by 50 %? The total weekly revenue (in dollars] of Country Workshop associated with manufacturing and selling their rolltop desks is given by the function R(x, y) =—0,2:c2 —0,25y2 —0,2x5v +200x+ 160 y where x denotes the number of finished units and )1 denotes the number of unfinished units manufactured and sold each week. The total weekly cost attributable to the manufacture of these desks is given by TC(x, y) = 100x + 70y + 4000 dollars. Determine how many finished units and how many unfinished units the company should manufacture and sell each week in order to maximize its weekly profit? What is the maximum profit realizable?

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Subject: Math
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