A firm's total cost function is: C = 6x2 - xy + 10y2 + 30, subject to the production quota x + y = 34. Construct the Lagrange function and solve for the equilibrium values. Calculate the total cost. What is the equilibrium value of x? What is the equilibrium value of y?     What is the equilibrium value of λ?     What is the optimized value of cost?

The marginal cost for a company to produce q items is given by MC(q)=0.004q2−0.6q+620. The​ company's fixed costs are ​$8500. Find the marginal cost at a production level of 400 items.   The marginal cost at a production level of 400 items is ??? per item.

Catalina Films produces video shorts using digital editing equipment (K) and editors (L). The firm has the production function Q(K, L)=KxL, where Q is the hours of edited footage. The wage is $25, and the rental rate of capital is $50. The firm wants to produce 3,000 units of output at the lowest possible cost.a) Find the marginal product of each input.b) Determine whether the production function exhibits diminishing marginal product to each input.c) Find the marginal rate of technical substitution(MRTSLK)d) How does MRTSLK change as more L, is used holding output constant.e) Find the least costly combination of labor and capital to produce 3000 units

A firm’s production is represented by the following function: Q = L1/4 K3/4 . The rental rate of capital (r) is $40 and the wage rate (w) is $12.a. For a given level of output, what should be the ratio of capital to labor in order to minimize costs?b. How much capital and labor should be used to produce 400 units of output? What is the total cost?c. What is the short run total cost if output is decreased to 300 units?d. How would the capital labor choice and total cost change in the long run?e. Would the firm prefer to relocate if input prices are r = 60 and w = 8 at an alternativelocation assuming relocation is costless?

Consider the following marginal cost function MC= 5 + 2qi. (a) Does the production process exhibits increasing returns? decreasing returns? constant returns? (b) If the price is $23. What’s the optimal production level? (c) If the price is $31. What’s the optimal production level?

A company manufactures a variety of camp stoves at different locations. The total cost C(x) (in dollars) of producing x camp stoves per week at plant A is shown in the figure. Discuss the graph of the marginal cost function C'(x) and interpret the graph of C'(x) in terms of the efficiency of the production process at this plant. C(x) $100,000 $50,000 500 1,000 Choose the correct answer below. A. The graph of y C'(x) shows that the marginal cost function is positive and decreasing. Since marginal costs are decreasing, the production process is becoming more efficient as production increases. B. The graph of y C'(x) shows that the marginal cost function is negative and decreasing. Since marginal costs are decreasing, the production process is becoming more efficient as production increases. C. The graph of y C'(x) shows that the marginal cost function is negative and increasing. Since marginal costs are increasing, the production process is becoming less efficient as production…