Find the only possible solution to the nonlinear programming problem max (200 - 6x² - 5y²) subject to 2x + 6y ≥ 300 ** =0.y* =0 (Round to two decimal places as needed.)
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- A firm has the production function: q = 20L04K0.8 With L=20 and K=24, what is the MRTS? Provide your answer to the nearest 1000th (0.001, or 3 decimal places). Do not forget to include the negative sign!Let C(T) be a function that models the dependence of the cost (C) in thousands of dollars on the amount of ore to extract from a copper mine measured in tons (T): 1) If you computed the average rate of change of cost with respect to tons for production levels between T = 20000 and T = 40000, give the units of your answer (no calculations - describe the units of the rate of change). 2) If you had a function for C(T) and were able to calculate the answer to part 1, explain why you would not expect your answer to be negative (explanation should be in terms of cost, tons of ore to extract, and rates of change).The output (Q) of a production process is a function of two inputs (L and K) and K is given by the following relationship: Q = 0.50LK− 0.10L2− 0.05K2 The per-unit prices of inputs L and K are $20 and $25, respectively. The firm is interested in maximizing output subject to a cost constraint of $500. Use the lagrangian optimization techniques to find the following: How many units of L and K should be used by the firm? What is the total output of this combination? What is the marginal rate of substitution between L and K?
- Hi, I have been trying to compute the optimal values from this lagrangian. But I can't seem to find a way to get the values from the answer key. I attached both the question and answers. Could you please explain to me how to get these values from the first-order conditions? Thank you very muchFor the following problem, what would be the objective function that aims at minimizing the total cost considering that X1, X2, X3, and X4 are the number of units produced and sold of Products 1, 2, 3, and 4, respectively? Manufacturing time (hr) per unit Machine Cost per hr ($) Product 1 Product 2 Product 3 Product 4 Capacity (hr). 10 2 4 2 500 5 3 1 2 380 4 7 1 450 Unit selling price ($) 75 45 O a. 20X1+30X2+40X3+20X4 O b. None of the answers OC. 75X1+70X2+55X3+45X4 Od. 63X1+52X2+53X3+34X4 123 دي دا فيا 70 2 55100VKL, where q is 4. The production function for puffed rice is given by q = the number of boxes produced per hour, K is the number of puffing guns used each hour, and L is the number of workers hired each hour. (a) Calculate the q = 1,000 isoquant for this production function and show it on a graph. (b) If K = 10, how many workers are required to produce q =1,000? What is the average productivity of puffed-rice workers? (c) Suppose technical progress shifts the production function to q = 200 VKL. Answer parts (a) and (b) for this new situation.
- The profit function in dollars for a product is given -x^3+76x^2-380x-2800 where x is the number of units produced and sold. If break even occurs when 10 units are produced and sold find a quadratic factor of the profit function and find a number of units other than 10 that gives break even for the product.A bitcoin miner, Alex, needs only electricity (E) and computer (K) to mine bitcoin. Assume that the production function for his bitcoin business is of Cobb-Douglas type,?(?,?)=???? with?+?< 1, resulting in strictly convex isoquants and is the same in South Korea and USA. Suppose that, similar to the podcast, the price per unit of electricity is higher in South Korea than in USA. Suppose that the price of a computer is the same in both countries. i. Determine whether it is more expensive to mine one bitcoin in South Korea than in USA based on the above assumptions by using appropriate diagram and explain your answer. Please keep electricity on the horizontal axis and computer on the vertical axis while drawing your diagram.A company uses two inputs, unskilled labour (L) and capital (K), to produce its product. The wage rate for a unit of labour is €5, while a unit of capital cost €20. a) Determine the equation and plot the isocost line for the company's expenditures on itsinputs of €1,000. Label the intercepts of the isocost with both axes. Draw a typical isoquant for an output level Q0 and indicate the optimal input levels of L and K. (Do not forget to label the axes). b) Suppose the government introduces a minimum wage for unskilled labour of €6 per unit.Show graphically and explain shortly how much it would cost the firm in the short run, with capital input fixed at K, to keep its output constant at Q0. c) Show graphically and comment shortly on the optimal factor mix that the firm would use to produce Q0 in the long run at the specified minimum wage of €6 per unit.
- AVC=10-0.03Q + 0.00005Q2TFC=60What is the TC function?What is the minimum AVC?The total cost (in hundreds of dollars) of producing x calculators per day is given by the equation. 20- 15- 10- C(x) = 6 + /2x + 32 Osx< 50 Perform the following calculations and interpret the results. 10 20 30 40 50 Production C'(x) =U %D Cost (hundred dollars)For each of the below production functions, find the minimum cost of producing 2 units of output when input prices are w₁ = 2 and W2 = : 5. Wherever rounding is needed, please round to 3 decimal points. (a) f(2₁, 22) = [min{z₁, 3z2}] = (b) f(21, 2₂) = 21+ 20.5.