Shows the derivative function of: TC = 4Q² + 2Q + DC(Q) + FC, where TC = Total Cost, DC = Depreciation cost of capital for each Q production, and FC = Fixed Cost.
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Shows the derivative function of:
TC = 4Q² + 2Q + DC(Q) + FC,
where TC = Total Cost, DC =
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- Company XYZ projects their revenues for the given quarter to be modeled by the function R(z) = 12z - 6z + 2000, where x represents the number of goods sold and R(x) the price. The fixed costs for Company XYZ include rent and wages, and is a total of 10000 each month and the variable costs for the quarter can be modeled by the function V (2) = 12x + 1000. (a) Find the break-even point for Company XYZ. [ Select) (b) Find the marginal profit function. I Select ](c) Consider the aggregate production function Y = K = 100,000, A = 8, and N = 128. K0.2 (AN)0.8 Compute output whenFor the following functions, show if they exhibit increasing, decreasing, or constant returns to scale using the proportionality factor t. 1 (a) q(L, K) = 2L K (c) q(L, K) = 3L+2K %3D %3D (b) q(L, K) = L² + K² (d) q(L, K) = }LK
- Paradise Pottery had the following costs in May when production is 800 ceramic pots: materials, $8,700; labor (variable), $2,900; depreciation, $1,100; rent, $900; and other fixed costs, $1,500. If production changes to 900 units, how much will the total variable costs and total fixed costs be, respectively?The cost formula for a company can be modeled by C=1092+40x+0.1x2C=1092+40x+0.1x2 where xx represents the number of items made. A formula for the company's income is modeled with R=108x−0.9x2R=108x-0.9x2, where xx is the number of items sold. A company will break even when its costs equal its income. How many items must a company make and then sell to break even? Answer: (If there are multiple answers, separate the answers with a comma.)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.
- It is assumed that the machine handles a flow rate of 0.5 million gallons per day. The cost of the machine is $1.24 million in 2020. The correlation exponent is 0.14. The cost index has been updated from 156 to 221 this year. The cost today for a flow of 2.3 million gallons per day is: a. $8,752,042 b. $2,175,081 c. $5,347,061 d. $3,562,455Consider the following production and cost functionsq=〖(10K^(2/5)+5L^(2/5))〗^(5/2)1250=20K+8LWhich implies〖MP〗_K=10〖(10K^(2/5)+5L^(2/5))〗^(3/2) K^(-3/5)〖MP〗_L=5〖(10K^(2/5)+5L^(2/5))〗^(3/2) L^(-3/5)What is the profit maximizing combination of K and L?Question 6 The estimation of a Cobb-Douglas production function for 20 firms of a given industry yields: = a. 16.907 + 0.322k; + 2.777lį R² = 0.915 DW = 2.032 RSS = 0.461 Use a = 5% Var ß = 0.166070 0.031857 0.216639 -0.857446 -0.057229 4.939971/ where : fitted values of naturals logaritrhms of output (output express in 1000 tons); ki: natural logaritrhms of capital output (output express in 1000 tons) li: natural logaritrhms of labour (labour is in hours) RSS: residual sum of squares 1: firm index Var ß: variance covariance matrix of estimates Evaluate the statistical significance of the coefficients. Page 4 of 12 b. A regression on the original regressors, q² and a constant term yields the following statistics: R² = 0.296041 F = 1.177507 coeff of ² has a t-statistic of 2.876 (i) With this information, which test can you implement to deal with the problem omitted variables and why? (ii) Implement the test as stated in b(i) and interpret the results. (iii) What is (are) the…
- A lawn service company has fixed monthly costs of $500 and variable costs (labor, gasoline, and depreciation) of $40 per lawn. If the service charges $60 per lawn,a. Write a cost function representing the cost C(x) to the company to service x lawns per month.b. Write a revenue function representing the revenue R(x) to service x lawns per month.c. Determine the number of lawns that must be serviced in a month for the company to break even.Let f(x1,x2)=xxx be a Cobb-Douglas production technology where a, ẞ> 0 and a+B< 1. (i) Show that the technology satisfies monotonicity, diminishing marginal product, diminishing TRS, and diminishing returns to scale. (ii) Which of these properties are invariant to arbitrary increasing transfor- mations of the technology? That is, which properties remain true for oof(x1, x2), where can be any strictly increasing function? You can assume that is differentiable for convenience. 2. Solve for the short-run profit maximization problem for f(x1, x2) = 2x1 + x2 and f(x1, x2) = min{2x1, x2}, holding x2 at 2, and taking real factor prices wi and w2 as given.Assume you were hired as a Production Engineer in a global Bearing Manufacturer company and given the following inputs: Equipment Maintenance Cost per Month Utilities Cost per Month Material Cost per Unit Labor Cost per Unit Selling Price per Unit S60,000.00 $12.000.00 $12.00 $3.00 $24.00 Calculate Total Fixed Cost per Month Calculate Total Variable Cost per Unit = Calculate number of Units to be sold to reach Break-Even Point = Calculate number of Units that must be sold to eam profit of $90,000.00