Question;Problem 1. Summer Job (6 pts).;Suppose you have just inheritedPhi'6,000 and you want to invest it. Upon hearing;thisnews, two;different portfolios have offered you an opportunity to become a partner in two;different;entrepreneurial ventures, one planned by each portfolio. In both cases, this;investmentwould involve;expending some of your time next summer as well as putting cash. Becoming afull partner in the first portfolio's venture;would require an investment of PhP 5,000 and 400hours, and your estimated profit (ignoring the;value of your time) would be PhP 4,500_ Thecorresponding figures For the second;portfolio's venture are Ph? 4,000 and 500 hours, with anestimated profit to you of Ph? 4,500. However;both portfolios are flexible and would allow you to come in at any fraction of;a full partnership you would like, your share of the profitwould be proportional to this fraction.;Because you;were looking for an interesting summer job anyway (maximum of 600hours), you have decided to participate in;one portfolio's or both portfolios' ventures inwhichever combination would maximize your;total estimated profit. You now need to solve theproblem of finding the best combination.;Formulate the linear programming modelFor this problem.;Answer;Subject to;Problem 2.Help the manager (6 pts).;An enterprisedecidednot to continue the production of unprofitable;product line Thisstrategy;caused huge excess in production capacity. The manager considered focusing theexcess capacity to one or more of three;products: X X2 and Xi. The available capacity on themachines that iniutit limit output is;presentedbelov,.;Machine tyke Available time kin machine hours per- week);F Milling;machine;Lathe 350;Grinder 1 150;The number of machine hours required for each;unit of the respective products is as follows;Productivity coefficients (in machine hours per unit);Machinetype;Product 1.;Milling.;machine;9;Lathe;5;Grinder;3;5;Product 2;4 0;3;The sales department indicates that the sales;potential for products 1 and 2 exceedsthemaximum production rate and that the sales;potential for product 3 is 20 units per week. Theunit profit for products 1, 2, and 3 would be;450, P20, and respectively. The manager'sobjective is to determine how much of each;product should he produced to maximize profit.Your goal is to formulate the linear;programming model for the manager;Answer;Subject to;Part 2. Parametric Models (20 points);Problem 4. Ordinary least Squares (OLS):(4 pts);Graduate;students under the course Quantitative Business Analysis at the University ofSanto Tomas were taught to encode qualitative data on men's hair;cut as: I, ii short trim, 2, if barber's, 3, if flat top, 4, if skinny;(skin-head), and 5, others. Running the qualitative data as dummy variable in their regression, they found;that the results were not according toexpectations because of wrong;model specification.;Help them encode properly the qualitative data. Dummy variable only (D);02;04;Problem 5.;Units sold: (3 pis);A marketing;representative establishes a regression equation for units sold based on thepopulation in the sales district and whether the district has a;home office to which the sales personnel report. The regression equation is;expressed as;17=;78.12 + 1.01X/ ? 17.2X2;Where;Y = units sold;Xi =population in thousandsX2 =dummy variable;Considering the above marketing;problem, if population is 17,000 in district containing an office and 17,000 in a district without an office, what would the;number of units sold ineach one be? First, properly encode the dummy;variable before answering the number of units sold in each district.;Answer;Dummyvariable,X2;Units sold in each district: Yw;YWO;Prp.blern 6.;Trend - Regression Analysis: (4 pts);One of the four elements of time series data;is trend, A trend is the long-run generaldirection of the business climate over the;periods of several years. Data trends can be;ascertained in several ways. One particular;technique is the regression analysis. In time series;trend-regression analysis, the response variable Y is the item being forecast;The independent;variable X;represents the time periods. Many possible trends can be explored with time;series;data. We will use only linear model and the quadratic model;because they are the easiest to understand;and simplest to compute.;A hypothetical data set of35years (1960 1994) regarding the;average length of the;work week in a particular country for the;furniture workers was run using the linear regressionanalysis. A regression line was fitted to the;35-year data by using the time period as theindependent variable (X) and length of work week as the dependent;variable (Y). The time periods are;consecutive that made it possible to renumbered them from 1 to 35 and enteredalong with the time series data (Y) into a;regression analysis.;The regression equation of the trend line is expressed as:11= 37.416;? 0.0614 + ei;where:Y ? work week (in hours) in furniture;industryX = time period;Fill the blank with the correct;answer;1. Give the average work week per year prior to the first year of;the data.;2, Predict the average work week on the year;1982.;3.;Forecast the average work week in the furniture industry for the year;2000.;4.;The average decline per year in work week in;the furniture industry.;Problem 8.;Stochastic Frontier Regression (SFR) model:(5pts);The Stochastic Frontier Regression concerns;with measuring frontiers which envelop data by maintaining the deterministic;portion of ordinary least square (OLS). The error term(ei) is decomposed into random error (YE) and technical;inefficiency (r,',). The 35;years data (1960 1994) of the furniture;industry in a hypothetical country was run into the SFR v. 4.1(Coelli;1992).;The derived SFR-LE trend equation is expressed as:17=;39.18-- 0.246X!+ 0.005X22+ (I, ? III};Where: Y ? work week (in hours) in the;furniture industry (not logged)Xi? time period;X22? time period squared;Vit;= random variables which are assumed to be iid N(0.av2), andindependent of the iii;tio ? are non-negative random variables which;are assumed to account fortechnical;inefficiency in production and are assumed to be lid as truncations at zero of the N(?,o-u2) distribution;Use the SFR-mic trend equation above to answer;problems 9 - 12.;5.;Give the average work week per year prior to the first year ofthedata.;6.;Predict the average work week on the year;2003.;7. Forecast the average work week in;the furniture industry for the year 2012.
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