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The production technology of a firm is estimated to be Q = 100N + 10N2 –...

The production technology of a firm is estimated to be Q = 100N + 10N2 – N3, where N is labor input and Q is output. The firm has a budget constraint on hiring labor that limits it to no more than 15 units of labor. a. Formulate the optimizing problem of the firm. b. Find the solution to the problem and find the optimum Q and N. c. Due to a restrictive labor market condition, the firm can not hire more than 8 units of labor. Find the optimum Q and N under new market conditions. d. What is the value of the Lagrange multiplier? What does it imply?

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