The production function for a product is given by Q = 100KL. If the price of capital is $120 per day and the price of labor is $30 per day, what is the minimum cost of producing 1000 units of output? The MPK = 100L and MPL = 100K.
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- General Account QuestionsA firm produces according to the following production function: F(L,K)=L0.7K0.3. The price of capital is $3 and the wage rate is $7. What is the optimal combination of labor and capital in order to produce 100 units of output? Multiple Choice L*=50,K*=50 L*=100,K*=50 L*=100,K*=100 L*=10,K*=10Suppose a firm with a production function given by Q = 30K0.5L0.5 produces 4,000 units of output. The firm pays a wage of $50 per unit and pays a rental rate of capital of $30 per unit. MPL = 15K0.5/L0.5 and MPK = 15L0.5/K0.5. How many units of labor and capital should the firm employ to minimize the cost of producing 4,000 units of output, and what would be the total cost?
- Suppose a ceiling fan manufacturer has the total cost function C(x) = 35x + 1200 and the total revenue function R(x) = 65x. (a) What is the equation of the profit function P(x) for this commodity? P(x) = (b) What is the profit on 20 units? P(20) = Interpret your result. The total costs are less than the revenue. The total costs are more than the revenue. The total costs are exactly the same as the revenue. (c) How many fans must be sold to avoid losing money? fans1) What level of output would generate a profit of $15,000 if a product sells for $24.99, has unit variable costs of $9.99, and total fixed costs of $55,005?i need the answer quickly
- 1. The function of a company's product to produce output at the level of input use is Q = -1/3x3 + 9x3 + 70. If the input price x used is IDR. 800, - per unit, while the output price is IDR. 10, - per unit, specify: a. The amount of input that must be used by the company in orderto produce the amount of output that provides maximum finance! How much is the output? b. What is the average size of the company?Suppose that when the output is 0, the total cost is 40. However, when the firm produces the first unit of output, the total cost is 50. Which of the following statements are true, which are false? The average cost of producing O True O False one unit is 25. The marginal cost of producing True False the first unit is 10. The fixed cost is 40. True False The variable cost of producing O True O False the first unit is 10.Let S represent the amount of steel produced (in tons). Steel production is related to the amount of labor used (L) and the amount of capital used (C) by the following function: S = 20 L0.30 C 0.70 In this formula L represents the units of labor input and C the units of capital input. Each unit of labor costs $50, and each unit of capital costs $100. (a) Formulate an optimization problem that will determine how much labor and capital are needed in order to produce 50,000 tons of steel at minimum cost. If your answer is zero, enter “0”. Min L + C s.t. L0.30 C 0.70 L, C (b) Solve the optimization problem you formulated in part a. Hint: When using Excel Solver, start with an initial L > 0 and C > 0. Do not round intermediate calculations. Round your answers to the nearest whole number. L = C = Cost = $
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