Linear Programming 1. While being enrolled at a local university, you want to work as a part-time employee at a local Walmart store. The pay rate at the Walmart store is $10 an hour. Since you have to invest a certain portion of time in your coursework, you can work as a part-time employee up to 20 hours a week. Suppose you want to decide how many hours you need to work for your part-time job to maximize your weekly earning, (a) Define the decision variable. (b) If you work 15 hours a week as a part-time employee, what's your weekly earning? (c) Develop a math expression for the weekly earing when you work x hours a week as a part-time employee (d) Develop a math expression for the constraint that limits the total number of hours you invest in your part-time job to 20 hours or less (e) By adding the non-negativity constraint, develop an LP model for maximizing your weekly earning. Maximize Subject to (0) Fill out the following table. Weekly Earning Hours Worked per week | Fusible Solution? 5 10 15 20 25 30 Minimize Subject to (8) Fill out the following table. Amount Spent Number of Round Feasible on Gasoline Trips per Week Solution? 21 3 41 5 6 81 (h) List all feasible solutions from the above table: (1) List all infeasible solutions from the above table 6) Find the optimal solution from the alwe table. 3. Financial Analysts, Inc. is an investment firm that mange stock portfolion for A mumber of clients. A new client is reqtasting that the firm handle an $80,00 portfolio As an initial investment strategy, the client would like to restrict the portfolio to a mix of the following two stock Auntil Return per Share Stock Oil Alanko Southwest Petroleum Price per Share 550 5:30 50 54 Let = number of shares of Oil Alaskan y = number of shares of Southwest Petroleum Financial Analysts, Inc. wants to maximize the total annual return on its investment (a) If Financial Analysts, Inc., purchases 20 shares of Oil Alaska stock and 70 shares of Southwest Petroleum stock, what is the expected annual return? (b) Assume that Financial Analysts, Inc., purchases I shares of Oil Alaskan stock and y shares of Southwest Petroleum stock Develop the mathematical expression for the total anual return. (e) If Financial Analysts, Inc., purchases 20 shares of Oil Alaskan stock and 70 sures of Southwest Petroleum stock, what is the total amount of fund invested into the two stocks? (d) Assume that Financial Analysts, Inc., purchases shares of Oil Alaska stock and y shares of Southwest Petroleum stock. Develop the mathematical expression for the constraint that says that the total amount of fund invested must be $800,000 or less (e) Assume thnt Financial Analysts, Inc, purchase shares of Oil Alaska stock and y shares of Southwest Petroleum stock Develop the mathematical expression for the constraint that says the amount of fund invested in Oil Alaska must be $500,000 or less (1) Assume thuat Pinancial Analyst Ine, purchash of Oil Alusa stock and y shares of Southwest Trofeum Mock Develop the mathematical expression for the contraint that says the amount of fund invested in Southwest Petroleum wat be less than or equal to $450,000 (g) Add the => 0 and y 20 constraints and provide a complete linear programming problem for the above investment problem. Maximize Subject to (h) Fill out the following table. Amount Total Amount Invested in Annual Amount Invested Southwest Feasible Return Invested in Oil Alaston Petroleum Solution? 10,000,00 10,000. 18.000 000 20000 4. Promo Time, a local advertising agency, has been buired to promote the waventure film Tomb Raiders starring Angle Harrison and Joe Lee Ford. The seney has been given a $100.000 budget to spend on advertising for the movie in the week prior to its release, and the movie's producer has dictated that only local television ads and locally targeted Internet ads will be used. Each television and cont 5500 and reaches an estimated 7000 people, and each Internet ad cost $250 and reaches an estimated 400 people. The movies producer has also dictated thatin der to avoid saturation no more than 20 television als will be placed. The producer has also stipulated that, in order to reach a critical ma, alanto Internet ads will be placed. The producer wants to determine how many television and internet de const be purchased in order to maximize the total number of people reached lw the advertisements Let mumber of television de parchased number of Internet de prend (A) Compute the tomber of people mach when Promotime pure 20 television add 100 Internet ads (b) Develop the mathematical expression for the total number of people reached when PromoTime purchases e television ads and y Internet ads. (c) Compute the total cost of advertising when Promotime purchases 20 television ads and 100 Internet ads. (d) Suppose that Promo Time purchases television ads and y Internet ads. Develop the mathematical expression for the constraint that says that the total cot of advertising must be $100.000 or los, (e) Suppose thut PromoTime purchases I television ads and y Internet ads. Develop the mathematical expression for the constraint that says the mimber of television ads should be less than or equal to 20. (1) Suppose that Promo Time purchases television ads and y Internet ads. Develop the mathematical expression for the constraint that is the mmber of Internet is should be 80 or more (2) Add the => 0 and 20 contraints anul provide a complete libent programming problem for the above situation Maximize Subject to (1) Pilt the following takde (h) Fill out the following table. 6 Number of People Reached Total Cost of Advertising Number of Number of Television Internet Ads Ads Feasible Solution? 10, y100 20, wy 5 EXTRA CREDIT Solve the linear programn you fornulated in Question 4 (8) using Excel Solver. Submit your Excel file. Linear Programming 1. While being enrolled at a local university, you want to work as a part-time employee at a local Walmart store. The pay rate at the Walmart store is $10 an hour. Since you have to invest a certain portion of time in your coursework, you can work as a part-time employee up to 20 hours a week. Suppose you want to decide how many hours you need to work for your part-time job to maximize your weekly earning, (a) Define the decision variable. (b) If you work 15 hours a week as a part-time employee, what's your weekly earning? (c) Develop a math expression for the weekly earing when you work x hours a week as a part-time employee (d) Develop a math expression for the constraint that limits the total number of hours you invest in your part-time job to 20 hours or less (e) By adding the non-negativity constraint, develop an LP model for maximizing your weekly earning. Maximize Subject to (0) Fill out the following table. Weekly Earning Hours Worked per week | Fusible Solution? 5 10 15 20 25 30 Minimize Subject to (8) Fill out the following table. Amount Spent Number of Round Feasible on Gasoline Trips per Week Solution? 21 3 41 5 6 81 (h) List all feasible solutions from the above table: (1) List all infeasible solutions from the above table 6) Find the optimal solution from the alwe table. 3. Financial Analysts, Inc. is an investment firm that mange stock portfolion for A mumber of clients. A new client is reqtasting that the firm handle an $80,00 portfolio As an initial investment strategy, the client would like to restrict the portfolio to a mix of the following two stock Auntil Return per Share Stock Oil Alanko Southwest Petroleum Price per Share 550 5:30 50 54 Let = number of shares of Oil Alaskan y = number of shares of Southwest Petroleum Financial Analysts, Inc. wants to maximize the total annual return on its investment (a) If Financial Analysts, Inc., purchases 20 shares of Oil Alaska stock and 70 shares of Southwest Petroleum stock, what is the expected annual return? (b) Assume that Financial Analysts, Inc., purchases I shares of Oil Alaskan stock and y shares of Southwest Petroleum stock Develop the mathematical expression for the total anual return. (e) If Financial Analysts, Inc., purchases 20 shares of Oil Alaskan stock and 70 sures of Southwest Petroleum stock, what is the total amount of fund invested into the two stocks? (d) Assume that Financial Analysts, Inc., purchases shares of Oil Alaska stock and y shares of Southwest Petroleum stock. Develop the mathematical expression for the constraint that says that the total amount of fund invested must be $800,000 or less (e) Assume thnt Financial Analysts, Inc, purchase shares of Oil Alaska stock and y shares of Southwest Petroleum stock Develop the mathematical expression for the constraint that says the amount of fund invested in Oil Alaska must be $500,000 or less (1) Assume thuat Pinancial Analyst Ine, purchash of Oil Alusa stock and y shares of Southwest Trofeum Mock Develop the mathematical expression for the contraint that says the amount of fund invested in Southwest Petroleum wat be less than or equal to $450,000 (g) Add the => 0 and y 20 constraints and provide a complete linear programming problem for the above investment problem. Maximize Subject to (h) Fill out the following table. Amount Total Amount Invested in Annual Amount Invested Southwest Feasible Return Invested in Oil Alaston Petroleum Solution? 10,000,00 10,000. 18.000 000 20000 4. Promo Time, a local advertising agency, has been buired to promote the waventure film Tomb Raiders starring Angle Harrison and Joe Lee Ford. The seney has been given a $100.000 budget to spend on advertising for the movie in the week prior to its release, and the movie's producer has dictated that only local television ads and locally targeted Internet ads will be used. Each television and cont 5500 and reaches an estimated 7000 people, and each Internet ad cost $250 and reaches an estimated 400 people. The movies producer has also dictated thatin der to avoid saturation no more than 20 television als will be placed. The producer has also stipulated that, in order to reach a critical ma, alanto Internet ads will be placed. The producer wants to determine how many television and internet de const be purchased in order to maximize the total number of people reached lw the advertisements Let mumber of television de parchased number of Internet de prend (A) Compute the tomber of people mach when Promotime pure 20 television add 100 Internet ads (b) Develop the mathematical expression for the total number of people reached when PromoTime purchases e television ads and y Internet ads. (c) Compute the total cost of advertising when Promotime purchases 20 television ads and 100 Internet ads. (d) Suppose that Promo Time purchases television ads and y Internet ads. Develop the mathematical expression for the constraint that says that the total cot of advertising must be $100.000 or los, (e) Suppose thut PromoTime purchases I television ads and y Internet ads. Develop the mathematical expression for the constraint that says the mimber of television ads should be less than or equal to 20. (1) Suppose that Promo Time purchases television ads and y Internet ads. Develop the mathematical expression for the constraint that is the mmber of Internet is should be 80 or more (2) Add the => 0 and 20 contraints anul provide a complete libent programming problem for the above situation Maximize Subject to (1) Pilt the following takde (h) Fill out the following table. 6 Number of People Reached Total Cost of Advertising Number of Number of Television Internet Ads Ads Feasible Solution? 10, y100 20, wy 5 EXTRA CREDIT Solve the linear programn you fornulated in Question 4 (8) using Excel Solver. Submit your Excel file