A small firm builds two types of garden shed. Garden shed 1 requires 2 hours machine time and 5 hours craftsman time. Garden shed 2 requires 3 hours of machine time and 5 hours of craftsman time. Each day there are 30 hours of machine time available and 60 hours of craftsman time. The profit one each garden shed 1 is £60 and, on each garden shed 2 is £84. Formulate the linear programming model and feasible solution using simplex method.
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Answer the following in 4 parts: • Provide the Linear Programming Model for each problem. • Solve the LP problems using simplex method. • Provide the final feasible solutions. • Create a spreadsheet model of the same problems using MS Excel Solver Add-In
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- Case 1: Western Chassis produces high-quality polished steel and aluminum sheeting and two lines ofindustrial chassis for the rack mounting of Internet routers, modems, and other telecommunicationsequipment. The contribution margin (contribution toward profit) for steel sheeting is $0.40 per poundand for aluminum sheeting is $0.60 per pound. Western earns $12 contribution on the sale of aStandard chassis rack and $15 contribution on a Deluxe chassis rack. During the next productioncycle, Western can buy and use up to 25,800 pounds of raw unfinished steel either in sheeting or inchassis. Similarly, 20,400 pounds of aluminum are available. One standard chassis rack requires 16pounds of steel and 8 pounds of aluminum. A Deluxe chassis rack requires 12 pounds of each metal.The output of metal sheeting is restricted only by the capacity of the polisher. For the next productioncycle, the polisher can handle any mix of the two metals up to 4,000 pounds of metal sheeting. Chassismanufacture…2. Provident Capital Corp. specializes in investment portfolios designed to meet the specific risk tolerances of its clients. A client contacted Provident with P2,000,000 available to invest. Provident’s investment advisor recommends a portfolio consisting of two investment funds: the Dynamic fund and the Diversified fund. The Dynamic fund has a projected annual return of 10%, and the Diversified fund has a projected annual return of 8%. The investment advisor requires that at most P1,400,000 of the client’s funds should be invested in the Dynamic fund. Provident’s services include a risk rating for each investment alternative. The Dynamic fund, which is the more risky of the two investment alternatives, has a risk rating of 6 per P40,000 invested. The Diversified fund has a risk rating of 4 per P40,000 invested. For example, if P400,000 is invested in each of the two investment funds, Provident’s risk rating for the portfolio would be 6(10) + 4(10) = 100. Finally, Provident developed…21. A linear programming problem has two constraints 2X + 4Y ≤ 100 and 1X + 8Y ≤ 100, plus nonnegativity constraints on X and Y. Which of the following statements about its feasible region is TRUE? Part 2 A. The graphical origin (0, 0) is not in the feasible region. B. The feasible region includes all points that satisfy one constraint, the other, or both. C. The feasible region cannot be determined without knowing whether the problem is to be minimized or maximized. D. The two corner points are (0, 0) and (50, 12.5). E. There are four corner points including (50, 0) and (0, 12.5)
- 1. Klara started working at a deli shop on April 1, 2020. On October 19, 2020 she informed her employer that she is pregnant and is due on February 1, 2021. Her employer informed her that they are not able to provide her any paid time off since it is a very small shop. They will, however, provide her with unpaid time off if she needs it. She has indicated that she would like to take her pregnancy leave starting November 2. Klara is concerned that the deli is hiring someone to replace her when she is on her leave. Which of the following is true: A. Klara has a right to her job back when her leave is over unless the position no longer exists for reasons other than Klara taking a leave. B. Klara is entitled to 17 weeks of pregnancy leave and up to 78 weeks of maternal leave. C. Klara is entitled to 17 weeks of pregnancy leave but all of her pregnancy leave Thust be taken before the birth of her baby D. Klara is entitled to 17 weeks of pregnancy leave and 63 weeks of parental leave. 2.…Case 2: A marketing research professor is conducting a telephone survey and needs to contact atleast 160 wives, 140 husbands, 110 single adult males, and 120 single adult females. It costs $2 tomake a daytime call and $4 (because of higher labor costs) to make an evening call. The table shownbelow lists the expected results. For example, 10% of all daytime calls are answered by a single male,and 15% of all evening calls are answered by a single female. Because of a limited staff, at most halfof all phone calls can be evening calls. Determine how to minimize the cost of completing thesurvey. Percentages Daytime Evening Wife 25% 25% Husband 15% 30% Single male 10% 25% Single female 15% 15% None 35% 5% Develop a Report for the following1) State the decision variables and constraints in this problem. 2) What is the objective function in this problem?…Case 2: A marketing research professor is conducting a telephone survey and needs to contact atleast 160 wives, 140 husbands, 110 single adult males, and 120 single adult females. It costs $2 tomake a daytime call and $4 (because of higher labor costs) to make an evening call. The table shownbelow lists the expected results. For example, 10% of all daytime calls are answered by a single male,and 15% of all evening calls are answered by a single female. Because of a limited staff, at most halfof all phone calls can be evening calls. Determine how to minimize the cost of completing thesurvey. Percentages Daytime Evening Wife 25% 25% Husband 15% 30% Single male 10% 25% Single female 15% 15% None 35% 5% Develop a Report for the following using the Solver application in Excel 4) Obtain a sensitivity report for the reported solution. Which constraints…
- Case 2: A marketing research professor is conducting a telephone survey and needs to contact atleast 160 wives, 140 husbands, 110 single adult males, and 120 single adult females. It costs $2 tomake a daytime call and $4 (because of higher labor costs) to make an evening call. The table shownbelow lists the expected results. For example, 10% of all daytime calls are answered by a single male,and 15% of all evening calls are answered by a single female. Because of a limited staff, at most halfof all phone calls can be evening calls. Determine how to minimize the cost of completing thesurvey. Percentages Daytime Evening Wife 25% 25% Husband 15% 30% Single male 10% 25% Single female 15% 15% None 35% 5% Develop a Report for the following using the Solver application on Excel 1) State the decision variables and constraints in this problem. 2) What is…2. A firm makes two products X and Y and has a total production capacity of 9 tons per day.X and Y requiring the same production capacity. The same has a permanent contract to supply at least two tons of X and at least 3 tons of Y per day to another company. Each ton of X requires 20 machine hours of production time and each ton of Y requires 50 machine hours of production time. The daily maximum possible number of machine hours is 360. The entire firm's output can be sold and profit made is 80 R.O of X and 120 R.O per ton of Y. It is required to determine the production schedule for maximum profit and to calculate this profit. Formulate a LPP.1. A city is reviewing the location of its fire stations. The city is made up of a number of neighborhoods, as illustrated in the figure below. A fire station can be placed in any neighborhood. It is able to handle the fires for both its neighborhood and any adjacent neighborhood (any neighborhood with a non-zero border with its home neighborhood). The objective is to minimize the number of fire stations used. Solve this problem. Which neighborhoods will be hosting the firestations?
- Chapter 8. Tyler bakes Cookies (C) and Breads (B) with the help of two ovens in his little bakery. The time taken by Oven A to bake each cookie batch is 14 minutes and the time taken by Oven B is 12 minutes. The time taken by Oven A to bake a batch of bread is 16 minutes and the time taken by Oven B is 17 minutes. Each week Oven A can be used for 28 hours, and Oven B can be used for 25 hours to bake Cookies and Breads. The rest of the time is used for baking other products. Moreover, Tyler starts the next week with a stock of 20 batches of Cookies and 20 batches of Breads. There is a weekly demand of 70 batches of Cookies and 35 batches of Breads. For each batch of Cookies, Tyler makes $15 in revenue and for each batch of Breads Tyler makes $20 in revenue. How should Tyler plan his production to maximize his revenue while meeting his weekly demand and adding to his stock for the following week? To help you guys out, I am giving you the Linear Program equations here. Using the Solver,…Chapter 8. Tyler bakes Cookies (C) and Breads (B) with the help of two ovens in his little bakery. The time taken by Oven A to bake each cookie batch is 14 minutes and the time taken by Oven B is 12 minutes. The time taken by Oven A to bake a batch of bread is 16 minutes and the time taken by Oven B is 17 minutes. Each week Oven A can be used for 28 hours, and Oven B can be used for 25 hours to bake Cookies and Breads. The rest of the time is used for baking other products. Moreover, Tyler starts the next week with a stock of 20 batches of Cookies and 20 batches of Breads. There is a weekly demand of 70 batches of Cookies and 35 batches of Breads. For each batch of Cookies, Tyler makes $15 in revenue and for each batch of Breads Tyler makes $20 in revenue. How should Tyler plan his production to maximize his revenue while meeting his weekly demand and adding to his stock for the following week? To help you guys out, I am giving you the Linear Program equations here. Using the Solver,…TOPIC: LINEAR PROGRAMMING (CASE WITH MORE THAN TWO VARIABLES FOR SIMPLEX METHOD)A company is considering the acquisition of additional machinery as part of a capital expansion program.expansion program. Four types of machines are being considered. The following table specifies the attributes pertinentto each of them: [Table]The total budget for the program is $6,000,000.00 and the maximum space available is 290 square meters.square meters. The company wants to maximize the production that will be achieved in the purchase of the new machines.B) What will be the maximum production?