Explain all the attachment
2. There is two goods X and Y. Their demand function is following; X=144-Px and Y=250-2Py the production quota is 2X+2Y=80 where cost of production is; C=2x2+ 2y-+ 2xy + 70, Now optimizes the profit. (a) maximize the profit. b) Now use the Bordered Hessian method to show that all the optimal values that you find in maximize the profit. c) Define the significance of Lagrange Multiplier in optimization using this context. What is the other name of Lagrange Multiplier? Please briefly discuss how it will affect a firm's decision in this context?5) Forecast November and December using the method you believe to be the most accurate. Question 2: Refer to the gasoline sales time series data in Table below to answer the following (Copy the file to Excel when done submit here) 1. Compute Three- week, four-week and five-week moving averages for the time series. 2. Compute the MSE for Three- week, the four-week and five-week moving average forecasts. (Look over the PowerPoint) 3. Create a new column to show the trend line (y- matb) for the table below 4. What appears to be the best number of weeks of past data (three, four. or five) to use in the moving average computation? 5. Plot gasoline sales time series after obtaining the contract with the Vermont state police 6. Plot gasoline sales time series and three-week moving average Forecasts 7. Plot gasoline sales time series and add the trend line to graph 121 1 words IN Type here to searchLab 5: Sampling Distribution of the Sample Mean X Write your name, class time, lab title and date. Print out commands and outputs, Make sure to answer all parts of each question and show work when possible. 1. Let's illustrate the idea of a sampling distribution in the case of a small sample from a small population. The population is the 32 students in Mr. Pineda's Math 120 course. A survey was done and they were asked multiple questions. One of the questions was: How much money did you spend this semester on books and materials for school? The results are under the variable "Money". Import the data set Math 120Survey available under the folder "Datasets" on Website and answer the following questions. a) Construct a histogram of the total money spent and titled it "Population Distribution." What is the overall shape of the distribution? b) Find the population mean, #, and population standard deviation, a, for the 32 students in the population. c) Use RStudio to draw 1000 random samples of size 5 from this population and calculate the mean for each. See example 1. You are approximationg the sampling distribution of X . Just print your code for this question since there is no output. d) Construct a histogram of the values you generated and titled it "Sampling Distribution". What is the overall shape of the distribution of X ? e) What are the sampling distribution mean and the standard deviation? How do they compare to the population mean and standard deviation in part (b)? 2. Total SAT scores of high school seniors are roughly Normal with a mean of 1026 and a standard deviation of 209. a) Julie scored 1110. What is her percentile? That is, she did better than what proportion of students? b) Now consider the scores of 30 randomly chosen students. What is the probability that their average score is more than 1 1 10? c) How high must a student score in order to place in the top 10% of all students taking the SAT?a) First, construct a graph showing the relationship between stock and growth, similar to Figure 18.2. Identify on your graph the stock levels that correspond to the maximum sustainable yield, and the stable and unstable equilibrium stock levels for this fish population in a natural state. b) Next, present a table showing the population growth rate, expressed as a percentage, at each stock level. For example, with a stock of 50,000 tons the annual growth is 2,800 tons, or 5.6 percent. What stock level maximizes the population growth rate? What point in Figure 18.1 does this growth rate correspond to (A, B, C, or D)? c) Suppose you are a resource manager overseeing this fishery. You want to ensure the ecological sustainability of the fishery by requiring that annual harvest should equal annual natural growth. You have collected data on the number of boat trips required to catch the annual growth of fish at different population stocks. This is given in the third column in the table above, which can be read from bottom to top to show increasing fishing effort. Assume that it costs $1,000 to operate a boat trip and that fish sells for $1,000 per ton. You must determine the annual quota for fish catch (in tons) and the population level you wish to maintain. What level of fishing effort maximizes economic efficiency while still being ecologically sustainable? Show your work. (Hint: Calculate industry revenues, costs, and profits for each level of fishing effort from 0 to 2,300.) Present a graph similar to Figure 18.3 showing total revenues and total costs to support your
