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- The cumulative learning curve coefficient CLCC(20, 0.8) is defined as follows:a. the cost to produce 20 units in a process with c(1) = 1 and a learning rate of 0.8.b. the cost to produce one unit in a process with c(1) = 20 and a learning rate of 0.8.c. the cost to produce one unit in a process with c(1) = 1 and a learning rate of 0.820.d. the cost to produce the 20th unit in a process with c(1) = 1 and a learning rateof 0.8.A strawberry growing company is deciding its production and sale plan for the national and international markets.The sale price for each ton of strawberry depends on the quantity offered in the market. If x1 tons is offered for the domestic market, the sale price will be (30 - x1) CU / ton, while if x2 tons is offered for the international market, the sale price will be (40 - x2) CU / ton.The cost for each ton of strawberry for the domestic market is 10 MU, while for the international market it is 15 MU.The company has the capacity to produce up to 10 tons of strawberries for sale and according to SAG restrictions, it must dedicate at least 10% of production to the international market.For technical production reasons, the company must additionally satisfy the following restriction: x12 + x22 ≤64.d) There is the option of buying new machinery to increase the production capacity of the company. In what range should the new machine increase production capacity to suit the company? How…A companies has invested $ 1 million in the purchase of new machinery in its plant and does not intend to incur major capital expenditure over the next two years. The companies can manufacture a product according to the annual production function: \ (Q (L) = 30L-L ^ 2 \) , while the annual labor costs (in $ 000's) of are given by the function \ (C (L (L ) = 4L ^ 2 + 20L \) . The companies sells the product at $ 10,000 per unit. a) Determine the optimal level of production and labor in order to maximize profits. b) Find annual profits. c) Calculate the present value of the net profit achieved during 2 years of production assuming an interest rate of 5%.
- A strawberry growing company is deciding its production and sale plan for the national and international markets.The sale price for each ton of strawberry depends on the quantity offered in the market. If x1 tons is offered for the domestic market, the sale price will be (30 - x1) CU / ton, while if x2 tons is offered for the international market, the sale price will be (40 - x2) CU / ton.The cost for each ton of strawberry for the domestic market is 10 MUs, while for the international market it is 15 MUs.The company has the capacity to produce up to 10 tons of strawberries for sale and, according to SAG restrictions, it must dedicate at least 10% of its production to the international market.For technical production reasons, the company must additionally satisfy the following restriction: x12 + x22 ≤64.a) Raise the NLP model that allows maximizing the net profit for the companyb) State the KKT conditions for the problem and indicate whether they are necessary and / or sufficient.c)…The production planner for Fine Coffees, Inc. produces two coffee blends: American (A) and British (B). He can only get 300 pounds of Colombian beans per week and 200 pounds of Dominican beans per week. Each pound of American blend coffee requires 12 ounces of Colombian beans and 4 ounces of Dominican beans, while a pound of British blend coffee uses 8 ounces of each type of bean. Profits for the American blend are $2.00 per pound, and profits for the British blend are $1.00 per pound. The goal of Fine Coffees, Inc. is to maximize profits.What is the weekly profit when producing the optimal amounts?Assume an electricity generator can produce electricity from two different production technologies, a dirty technology and a clean technology. The quantity of electricity produced from the dirty technology is Qd in megawatt hours (MWh) and the amount from the clean technology is Qc. The dirty technology produces carbon emissions at a constant rate of d tons per MWh of electricity generation. The clean technology produces carbon emissions at a constant rate of c tons per MWh, where Bc < Bd. The cost functions for the two generation technologies are C(Qd) and C(Qc). The market price of electricity is P. Under these assumptions, the firm’s profit function is: Profit = PQd + PQc - C(Qd) - C(Qc). 1.) Take the partial derivative of profit with respect to each output (Qd and Qc) and set each equal to zero to find the profit maximizing (“first-order”) conditions for each type of electricity. Denote marginal costs of each type of electricity as MCd and MCc. Write down and interpret…
- Consider the following Cobb-Douglas production function for the bus transportation system in a city: Q = Lβ1Fβ2Bβ3 Where L = labour input in worker hours F = fuel input in gallons B = capital input in number of buses Q = output measured in millions of bus miles Suppose that the parameters (α, β1, β2 and β3) of this model were estimated using annual data for the past 25 years. The following results were obtained: β1 = 0.45, β2 = 0.20 and β3 = 0.30 a. Determine the (i) labour, (ii) fuel, and (iii) capital-input production elasticitiessuppose an industry consists of 10 identical firms with no fixed cost and marginal cost equal to MCi = 2qi (e.g., the marginal cost of the 20th unit is $40, the marginal cost of the 200th unit is $400, etc.). Further, suppose that the market demand in the industry is P = 840 - .5Q, where Q = ∑qi is the aggregate quantity from all 10 identical firms. Finally, ignore the possibility of new entrants beyond the 10 current firms. Maintaining the same assumptions as in the prior question, suppose now that the 10 firms collude and set quantity to maximize industry profits. Assuming that the 10 firms each produce an equal amount, how much will each firm produce this collusive equilibrium? Give typed answer correctly with proper explanation ASAPGiven a Cobb-Douglas production function estimate of Q = 1.19L.72K.18 for a given industry, this industry would have:
- Consider the following Cobb-Douglas production function for the bus transportation system in a city: Q = Lβ1Fβ2Bβ3Where L = labour input in worker hours F = fuel input in gallons B = capital input in number of buses Q = output measured in millions of bus miles Suppose that the parameters (α, β1, β2 and β3) of this model were estimated using annual data for the past 25 years. The following results were obtained: β1 = 0.45, β2 = 0.20 and β3 = 0.30a. Determine the (i) labour, (ii) fuel, and (iii) capital-input production elasticities .b. Suppose that labour input (worker hours) is increased by 2 percent next year (with the other inputs held constant), determine the approximate percentage change in output. c. Suppose that capital input (number of buses) is decreased by 3 percent next year (which, certain older buses are taken out of service). Assuming that the other inputs are held constant, determine the approximate percentage change in output. d. What type of returns to scale appears…A hypothetical company located in the Asia Pacific region is an integrated wood industry company which manages over 800,000 hectares of natural forest and 50,000 hectares of industrial timber plantations. The company also has two plywood factories and two Medium Density Fibreboard factories with a total production capacity of 200,000m3 per year. It exports over 85% of its product to more than 15 countries in 5 continents. Plywood production consists requires energy, water, and use of some industrial chemicals. The process produces emissions into water and air. The company is aware that its operations have multiple social and environmental impacts, especially relating to forest preservation and air and water quality. The company decides to implement ISO 14001. What benefits could the company derive from certification under ISO 14001? Relate to the ISO certification of a wood-based company in a real world.Given: Q = -0.0250 L3 + 1.5 L2 The chief economist for Argus Corporation, a large appliance manufacturer, estimated the firm’s short-run cost function for vacuum cleaners using an average variable cost function of the form AVC = a + bQ + cQ2 where AVC = dollars per vacuum cleaner and Q = number of vacuum cleaners produced each month. The total fixed cost each month is $180,000. The following results in the picture were obtained: a) Are the estimates ˆa, ˆb, and cˆ statistically significant at the 2 percent level of significance? Which is/are significant and which is/are not?b) Do the results indicate that the average variable cost curve is ∪-shaped? How do you know? c) If Argus Corporation produces 8,000 vacuum cleaners per month, what is the estimated average variable cost? Marginal cost? Total variable cost? Total cost? d) Answer part c, assuming that Argus produces 10,000 vacuum cleaners monthly. e) At what level of output will average variable cost be at a minimum? What is…