Statistics Questions Need Excel Spreadsheet Filled Out

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goevryyr

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I need the questions (mat 540 hw wk7) answered on the HW7 Answer Sheet.

Complete the following problems from Chapter 3:

  • Problem 8 (solve using the computer), 10, 11 (solve using the computer), 12, 14, 15, 16, 18, 24


mat540 hw wk7 (1).docx HW7_answer_sheet.xlsx 

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MAT540 Homework Week 7 Page 1 of 4 MAT540 Week 7 Homework Chapter 3 8. Solve the model formulated in Problem 7 for Southern Sporting Goods Company using the computer. a. State the optimal solution. b. What would be the effect on the optimal solution if the profit for a basketball changed from $12 to $13? What would be the effect if the profit for a football changed from $16 to $15? c. What would be the effect on the optimal solution if 500 additional pounds of rubber could be obtained? What would be the effect if 500 additional square feet of leather could be obtained? Reference Problem 7. Southern Sporting Good Company makes basketballs and footballs. Each product is produced from two resources rubber and leather. The resource requirements for each product and the total resources available are as follows: Product Basketball Football Total resources available Resource Requirements per Unit Rubber (lb.) Leather (ft2) 3 4 2 5 500 lb. 800 ft2 10. A company produces two products, A and B, which have profits of $9 and $7, respectively. Each unit of product must be processed on two assembly lines, where the required production times are as follows: Hours/ Unit Product Line 1 Line2 A 12 4 B 4 8 Total Hours 60 40 a. Formulate a linear programming model to determine the optimal product mix that will maximize profit. b. Transform this model into standard form. MAT540 Homework Week 7 Page 2 of 4 11. Solve problem 10 using the computer. a. State the optimal solution. b. What would be the effect on the optimal solution if the production time on line 1 was reduced to 40 hours? c. What would be the effect on the optimal solution if the profit for product B was increased from $7 to $15 to $20? 12. For the linear programming model formulated in Problem 10 and solved in Problem 11. a. What are the sensitivity ranges for the objective function coefficients? b. Determine the shadow prices for additional hours of production time on line 1 and line 2 and indicate whether the company would prefer additional line 1 or line 2 hours. 14. Solve the model formulated in Problem 13 for Irwin Textile Mills. a. How much extra cotton and processing time are left over at the optimal solution? Is the demand for corduroy met? b. What is the effect on the optimal solution if the profit per yard of denim is increased from $2.25 to $3.00? What is the effect if the profit per yard of corduroy is increased from $3.10 to $4.00? c. What would be the effect on the optimal solution if Irwin Mils could obtain only 6,000 pounds of cotton per month? Reference Problem 13. Irwin Textile Mills produces two types of cotton cloth – denim and corduroy. Corduroy is a heavier grade of cotton cloth and, as such, requires 7.5 pounds of raw cotton per yard, whereas denim requires 5 pounds of raw cotton per yard. A yard of corduroy requires 3.2 hours of processing time; a yard of denim requires 3.0 hours. Although the demand for denim is practically unlimited, the maximum demand for corduroy is 510 yards per month. The manufacturer has 6,500 pounds of cotton and 3,000 hours of processing time available each month. The manufacturer makes a profit of $2.25 per yard of denim and $3.10 per yard of corduroy. The manufacturer wants to know how many yards of each type of cloth to produce to maximize profit. Formulate the model and put it into standard form. Solve it. 15. Continuing the model from Problem 14. a. If Irwin Mills can obtain additional cotton or processing time, but not both, which should it select? How much? Explain your answer. b. Identify the sensitivity ranges for the objective function coefficients and for the constraint quantity values. Then explain the sensitivity range for the demand for corduroy. MAT540 Homework Week 7 Page 3 of 4 16. United Aluminum Company of Cincinnati produces three grades (high, medium, and low) of aluminum at two mills. Each mill has a different production capacity (in tons per day) for each grade as follows: Aluminum Grade High Medium Low Mill 1 6 2 4 2 2 2 10 The company has contracted with a manufacturing firm to supply at least 12 tons of high-grade aluminum, and 5 tons of low-grade aluminum. It costs United $6,000 per day to operate mill 1 and $7,000 per day to operate mill 2. The company wants to know the number of days to operate each mill in order to meet the contract at minimum cost. a. Formulate a linear programming model for this problem. 18. Solve the linear programming model formulated in Problem 16 for Unite Aluminum Company by using the computer. a. Identify and explain the shadow prices for each of the aluminum grade contract requirements. b. Identify the sensitivity ranges for the objective function coefficients and the constraint quantity values. c. Would the solution values change if the contract requirements for high-grade alumimum were increased from 12 tons to 20 tons? If yes, what would the new solution values be? 24. Solve the linear programming model developed in Problem 22 for the Burger Doodle restaurant by using the computer. a. Identify and explain the shadow prices for each of the resource constraints b. Which of the resources constrains profit the most? c. Identify the sensitivity ranges for the profit of a sausage biscuit and the amount of sausage available. Explain these sensitivity ranges. Reference Problem 22. The manager of a Burger Doodle franchise wants to determine how many sausage biscuits and ham biscuits to prepare each morning for breakfast customers. The two types of biscuits require the following resources: Biscuit Labor (hr.) Sausage (lb.) Ham (lb.) Flour (lb.) Sausage 0.010 0.10 --0.04 Ham 0.024 --0.15 0.04 The franchise has 6 hours of labor available each morning. The manager has a contract with a local grocer for 30 pounds of sausage and 30 pounds of ham each morning. The manager also MAT540 Homework Week 7 Page 4 of 4 purchases 16 pounds of flour. The profit for a sausage biscuit is $0.60; the profit for a ham biscuit is $0.50. The manager wants to know the number of each type of biscuit to prepare each morning in order to maximize profit. Formulate a linear programming model for this problem. Sporting Goods Resource Requirements per Unit (1) Product Basketball Football Resource Requirements per Unit (2) 2 Rubber (lb.) 3 2 Leather (ft ) 4 5 500 800 Basketball 12 Football 16 Product Basketball Football 2 Rubber (lb.) 3 2 Leather (ft ) 4 5 500 800 Basketball 13 Football 15 input Constraint s Total resources available Profits ($) Basketball Football Basketball Football input Objective function Rubber (lb.) 3 2 Maximized profits (3b) Resource Requirements per Unit Product Basketball Football input Constraint s Profits ($) Decision variables Maximized profits (3a) Total resources available 2 Leather (ft ) 4 5 Resource Requirements per Unit Product Basketball Football Rubber (lb.) 3 2 2 Leather (ft ) 4 5 Total resources available Profits ($) Basketball Football Maximized profits Total resources available 1000 800 Basketball 12 Football 16 Profits ($) Decision variables Basketball Football input Objective function Please use computer method to solve the problem Please enter your solution in Yellow cells Maximized profits 500 1300 Basketball 12 Football 16 A & B products Hours/ Unit Line 1 Line2 12 4 4 8 Product A B Constraints Total Hours Profits ($) Product A Product B Maximized profits 60 40 A 9 B 7 decision variables Objective function A & B products (1) (2a) Hours/ Unit Line 1 Line2 12 4 4 8 Product A B Product A B Hours/ Unit Line 1 Line2 12 4 4 8 Constraints Total Hours Profits ($) 40 40 A 9 B 7 Product A Product B decision variables Maximized profits (2b) Objective function Hours/ Unit Line 1 Line2 12 4 4 8 Product A B Total Hours Profits ($) Product A Product B Maximized profits 60 40 A 9 B 20 Total Hours 60 40 Profits ($) A 9 B 15 Product A Product B Maximized profits Please run sensitivity analysis on P10 and enter the results (changes in coefficients of the objective function, and shadow prices) in YELLOW cells Sensitivity analysis Product A Product B Shadow price Line 1 Line 2 Min Max Coefficients in the objective function (profits for A and B) Additional Profits Irwin textile mills Profits for each product Corduroy 3,1 denim 2,25 7,5 3,2 5 3 Resources Cotton Labor
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Just what I needed…Fantastic!

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