The wage rate is 40 per unit of labor the rental rate

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term is units of capital raised to the -25 power. The wage rate is \$40 per unit of labor. The rental rate is \$120 per unit of capital. The output quota is 300 units. Question: How many units of labor minimize cost? 5,000 units 300 units 10,000 units 3,000 units 1,000 units 8,000 units 1,250 units 4,250 units Givens: 40 * L + 120 * K min L>0, K > 0 s.t. 300 < K.75 * L 25 The marginal product of labor: MPL = .25 * * The marginal product of capital: MPK = .75 * 7:23 Equation Description: A firm is attempting to minimize total cost
subject to sufficiently employing units of labor and units of capital to produce an output level at least as large as a specified output quota. Total cost equals the cost to employing units of labor plus the cost to employing units of capital. A firm's production function is the product of two terms: the first term is units of capital raised to the.75 power; and, the second term is units of labor raised to the 25 power. The marginal product of labor equals the product of three terms: the first term is.25; the second term is units of capital raised to the 75 power; the third term is units of labor raised to the -75 power. The marginal product of capital equals the product of three terms: the first term is.75; the second term is units of labor raised to the 25 power; the third term is units of capital raised to the -25 power. The wage rate is \$40 per unit of labor. The rental rate is \$120 per unit of capital. The output quota is 300 units. Question: How many units of capital minimize cost? 5,000 units 300 units 4,250 units

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