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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- Suppose 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? fansThe cost equation of YTS Inc. is y = 35x + 400,000. y is the profit, 35 is the contribution margin per unit, x is the number of units sold, and 400,000 is the total fixed cost. What is the total units to be sold to arrive a profit of 146,000?
- Suppose the wage rate is $10 and the rental rate on capital is $20. Consider the total cost line associated with a total cost of $200. The intercept of this line on the Y-axis (capital axis) is _______ and its slope is_____. A. 10, -1/2 B. 20, -1/2 C. 10, -2 D. 20, -21) 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?A company produces and sells a product. The company has found that the costto produce x units of the product is given by C(x) = 50x + 200 (in dollars),and the revenue from selling x units is given by R(x) = 100x - x? (in dollars).What is the number of units the company should produce and sell to maximize profit
- The revenue for selling x units of a product is R = 150x. The cost of producing x units is C = 125x + 800. For what values of x will this product generate a profit?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 the marginal cost and marginal revenue (in ¢000) for a product produced by a company is estimated to be MC=q+35 MR=560+22q-q^2 Where q is the quantity produced and the firm’s break-even is 5 units per week You are Required to I. determine the total cost and the total revenue function in terms of q. II. estimate the output at which profit is maximize III. calculate the maximum profit
- 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 = $A firm has a cost function C(x)=10x+107, where x represents the number of units produced. the firm's revenue function is R(x)=38x if x is equal to 78 find the firm's profit. round to the nearest whole number