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- = 2. The cost of operating a jet-powered commercial (passenger- carrying) airplane varies as the three-halves (3/2) power of its velocity; specifically, Co kny3/2, where n is the trip length in miles, k is a constant of proportionality, and vis velocity in miles per hour. It is known that at 400 miles per hour, the average cost of operation is $300 per mile. The company that owns the aircraft wants to minimize the cost of operation, but that cost must be balanced against the cost of the passengers' time (CC), which has been set at $300,000 per hour. At what velocity should the trip be planned to minimize the total cost, which is the sum of the cost of operating the airplane and the cost of passengers' time?A company produces and sells luxury goods and is able to control the demand for the product by varying the selling price. The relationship between price and demand is found to be: p=10-(42/D^2)+2Dwhere p is the price per unit in million dollars and D is the demand per year. The company is seeking to maximize its profit. The fixed cost is $59 million per year and the variable cost is $25 million per unit. The production capacity is 42 units per year, and the company produces at least 1 unit per month.a) Derive how to find the number of units that should be produced annually to maximize profit.b) What is the maximum profit per year?c) What is the annual breakeven point?d)What is the company’s range of profitable output per year?A company produces and sells luxury goods and is able to control the demand for the product by varying the selling price. The relationship between price and demand is found to be: p=10-(42/D^2)+2Dwhere p is the price per unit in million dollars and D is the demand per year. The company is seeking to maximize its profit. The fixed cost is $59 million per year and the variable cost is $25 million per unit. The production capacity is 42 units per year, and the company produces at least 1 unit per month. 1) What is the company’s range of profitable output per year?
- The country of Luberia has discovered a massive oil field. Many companies have acquired rights to drill wells in the field. Oil engineers have calculated that the total output of oil per year (in barrels) will be Q = 1000n - n? where n is the number of wells drilled. Oil sells for $50 per barrel and a well costs $10,000 per year to drill and maintain. (a) What would be the equilibrium number of wells drilled if entry is uncontrolled? What will be the total output of oil and the net surplus generated for the economy? (b) Suppose the government nationalizes the oil industry. How many wells should be drilled to maximize surplus? How much surplus is generated? (c) Can government achieve the outcome in (b) without nationalizing the industry? How? Give a detailed answer.Suppose that the production function is given by Y=AK0.4N0.6. What is the percentage change in output if TFP declines by 43%? Write the answer in percent terms with up to two decimals (e.g., 10.22 for 10.22%, or 2.33 for 2.33%).The following figure shows the incremental cost of two units and the marginal cost (old) of the system, when all constraints are met. If both units were dispatched at their minimum values, what would be the marginal cost of the new system (new)? Select one: a The incremental cost of unit 1 Ob. Approximately 46.3 $/MWh S/MWh 49 48 C1=45+0.02Pg1 47 46 45 44 C2=43+0.006Pg2 I C. The incremental cost of unit 2 0 100 200 300 400 500- 600 MW
- Consider 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?Oil prices have increased a great deal in the last decade. The following table shows the average oil price for each year since 1949. Many companies use oil products as a resource in their own business operations (like airline firms and manufacturers of plastic products). Managers of these firms will keep a close watch on how rising oil prices will impact their costs. The interest rate in the PV/FV equations can also be interpreted as a growth rate in sales, costs, profits, and so on. Year 1949 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 per barrel $ 2.54 $ 2.51 $2.53 $ 2.53 $ 2.68 $2.78 $ 2.77 $ 2.79 $ 3.09 $ 3.01 $ 2.90 $ 2.88 $ 2.89 $2.90 $ 2.89 $ 2.88 $2.86 $ 2.88 $ 2.92 $ 2.94 Year 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1997 198 Annual growth rate Average Oil Prices per barrel $ 3.09 $3.18 $3.39 $3.39 $ 3.89 $ 6.87 Year 1989 1990 1991 1992 1993 1994 $ 7.67 1995 $8.19 1996 $ 8.57…10K L%. 1). Consider the production function Q = (a) What is the output when K = 100000 and L = 243? (b) Use the marginal analysis to estimate Q(99995, 243) and Q(100000, 245). (c) Use a calculator to compute these two values of Q to three decimal places and compare these values with your estimates in (b). (d) How big must AL be in order for the difference between Q(100000, 243+AL) and its linear approximation Q(100000, 245) + -DAL, to differ by more than two units?
- %3D A manufacturer has determined the marginal-cost function dc/dq below, where q is the number of units produced. If marginal cost is $70.00 when q = 50 and fixed costs are $5000, what is the average cost of producing 500 units? dc = 0.012q - 0.4q + 60 dq The average cost of producing 500 units is $(i) A business manager determines that t months after production begins on a new product,the number of units produced will be P thousand, where P(t) =6?2 + 5?(? + 1)2.What happens to production in the long run ?(ii) A ruptured pipe in a North Sea oil rig produces a circular oil slick that is y meters thick at adistance x meters from the rupture. Turbulence makes it difficult to directly measure thethickness of the slick at the source (where x = 0), but for x > 0, it is found thaty =0.5(x2 + 3x)x3 + x2 + 4x . Assuming the oil slick is continuously distributed, howthick would you expect it to be at the source?An Apple Cars plant operates most efficiently (average unit cost is minimized) when producing 18,300 cars each month. It has a maximum output capability of 22,000 units per month (e.g., when its CEO, Tim Chef, forces everyone to work crazy amounts of overtime), and can make as few as 7,000 units per month without forcing the hand of executives to shift production to another plant. If the plant makes 12,770 cars in December, what was the capacity utilization rate? Round your final answer to 1 decimal place, and enter it as a percent without the percent sign; for example, use 18.9, not 18.9% or .2. Capacity utilization rate