MM510 F15 Applications of Linear Programming HW Due: Sept 18, 2015 For this assignment, you should formulate and solve each problem in a separate worksheet of an excel workbook. Upload the excel workbook to Moodle as your solution to the assignment. 1) Note: This problem appears on page 726 in the textbook as problem 1 in chapter 14. You should use your completed Postal Employees linear program from the module workbook as a starting point. Modify the post office model so that employees are paid $10 per hour on weekdays and $15 per hour on weekends. Change the objective so that you now minimize the weekly payroll. (You can assume that each employee works eight hours per day.) Is the previous optimal solution still optimal? 2) Note: This problem appears on page 727 in the textbook as problem 5 in chapter 14. You should use your completed Postal Employees linear program from the module workbook as a starting point. In the post office example, suppose that the post office can force employees to work one day of overtime each week on the day immediately following this five-day shift. For example, an employee whose regular shift is Monday to Friday can also be required to work on Saturday. Each employee is paid $100 a day for each of the first five days worked during a week and $135 for the overtime day (if any). Determine how the post office can minimize the cost of meeting its weekly work requirements. 3) Walton Adams owns and operates Walton Adams Market, a convenience store in Rochester, Michigan. Walton Adams Market sells newspapers, non-perishable groceries and lottery tickets. Few of his customers buy more than a handful of items on a single visit and nearly half buy only one item such as a newspaper, cigarettes or a soda. Recently, Walton installed three rows of shelves near the cash register. He planned to use the new shelf space to promote the sale of impulse items like 2-liter bottles of soft drinks, popcorn, and potato chips. In the two months since the shelves had been installed Walton had experimented with different items on the shelves and with different placements. He had found the top shelf attracted the most attention and the bottom shelf the least. It seemed unwise to place more than three items on a single shelf; any more would take away some of the impact and would also lead to frequent restocking. Partly on the basis of his limited experimental data and partly on guesswork, Walton estimated the weekly contribution he could expect from a product as a function of the shelf it was on. The contribution amounts are shown in the table below. The various products would be carried in their usual locations in the store as well as on the new shelf; therefore, the values represent Weekly Contribution if on Shelf the weekly contribution net of the cannibalizing Product 1 2 3 effect on existing sales. A B C D E F G H I J K L 79 76 73 69 66 56 51 47 43 42 36 35 46 62 47 52 53 38 35 32 35 39 28 20 45 43 42 32 30 24 20 15 28 19 22 14 Page: 1 of 2 QMM510 F15 Applications of Linear Programming HW Due: Sept 18, 2015 a) Formulate a linear program to determine how to place the products on the shelves: Determine the decision variables; Develop the objective function; Define the constraints. b) Input the linear program into Excel. Use solver to determine product placement to maximize contribution. c) Obtain the Sensitivity Report. Short Answer: How would you interpret the reduced costs, i.e., what do they tell you in the context of product placement. 4) Note: This problem appears on page 704 in the textbook as problem 22 in chapter 13. You should use your completed six month production plan linear program from the module workbook as a starting point. Modify the Pigskin spreadsheet model so that demand in any of the first five months must be met no later than a month late, whereas demand in month 6 must be met on time. For example, the demand in month 3 can be met partly in month 3 and partly in month 4. How does this change the optimal production schedule? How does it change the optimal total cost? Page: 2 of 2 Product A B C D E F G H I J K L Weekly Contribution if on Shelf 1 2 3 79 46 45 76 62 43 73 47 42 69 52 32 66 53 30 56 38 24 51 35 20 47 32 15 43 35 28 42 39 19 36 28 22 35 20 14