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H w N 5 1 B C D E F G 1 X1 X2 # of X-pods of Blueberrys 3 4 Unit Profits 5 6 Total Profit 7 Used Sign Available Slack 8 Electronic 9 Assembly 10 11 12 Glickman Electronics Example 13 The Glickman Electronics Company in Washington, DC, produces two products: (1) the 14 Glickman x-pod and (2) the Glickman BlueBerry. The production process for each product is 15 similar in that both require a certain number of hours of electronic work and a certain number 16 of labor-hours in the assembly department. Each x-pod takes 4 hours of electronic work and 17 2 hours in the assembly shop. Each BlueBerry requires 3 hours in electronics and 1 hour in assembly. During the current production period, 240 hours of electronic time are available, 18 and 100 hours of assembly department time are available. Each x-pod sold yields a profit 19 of S7: each BlueBerry produced may be sold for a $5 profit. 20 Glickman's problem is to determine the best possible combination of x-pods and BlueBerrys to manufacture to reach the maximum profit. This product-mix situation can be 21 formulated as a linear programming problem. 22 We begin by summarizing the information needed to formulate and solve this problem (see 23 Table B.1). Further, let's introduce some simple notation for use in the objective function and constraints. Let: 24 25 X number of x-pods to be produced 26 X = number of Blue Berrys to be produced 2 NNN L X5 7pm G H x6 11pm LHS Wichita's famou shift The followi Sign RHS > Decision vara X, numi XXX B c D E x1 X2 x3 X4 Start to work at 3am 7am 11am 3pm 3 Work within 4 Period 1 (3am - 7am) 5 Period 2 (7am - 11am) 6 Period 3 (11am - 3pm) 7 Period 4 (3pm - 7pm) 8 Period 5 (7pm - 11pm) 9 Period 6 (11pm - 3am) 10 11 Total # of Employees 12 13 Unit Costs (per hour/ per server) $ 20 $ 18 S 16 S 18 14 15 Total Cost 16 17 1B 19 20 21 22 23 Scheduling Question Owner Avanti Seth's required for one day $ 20 $ 24 RENOW View Developer Help Power Pivot K M N R S T V Wichita's famous Sethi Restaurant is open 24 hours a day. Servers report for duty at 3 AM 7AM 11 AM 3PM 7PM or 11 PM, and each works an 8-hour shit. The following table shows the minimum number of workers needed during the 6 periods into which the day is divided Decision vairable X, number of workers reporting for the start of working period where / 1.2.3.4.5. or 6. Period Time Number of Servers Required 3 AM - 7AM 2 7 AM - 11 AM 14 3 11 AM - 3 PM 15 4 3PM - 7PM 10 5 7 PM - 11 PM 5 11 PM-AM 5 Oines Avant Seth's scheduling problem is to determine how many servers should report for work at the start of each time period in order to minimize the total stal required for one day's operation in Lut , equal the number of servers beginning work in time period, where - 1,2,34,5,6) D E F G H AU N 1 X1 X2 2 # of X-pods of Blueberrys 3 4 Unit Profits 5 6 Total Profit 7 Used Sign Available Slack 8 Electronic 9 Assembly 10 11 12 Glickman Electronics Example 13 The Glickman Electronics Company in Washington, DC, produces two products: (1) the 14 Glickman x-pod and (2) the Glickman BlueBerry. The production process for each product is 15 similar in that both require a certain number of hours of electronic work and a certain number 16 of labor-hours in the assembly department. Each x-pod takes 4 hours of electronic work and 17 2 hours in the assembly shop. Each Blue Berry requires 3 hours in electronics and 1 hour in assembly. During the current production period, 240 hours of electronic time are available, 18 and 100 hours of assembly department time are available. Each x-pod sold yields a profit 19 of S7: each BlueBerry produced may be sold for a $5 profit. 20 Glickman's problem is to determine the best possible combination of x-pods and 21 BlueBerrys to manufacture to reach the maximum profit. This product-mix situation can be formulated as a linear programming problem. 22 We begin by summarizing the information needed to formulate and solve this problem (see 23 Table B.1). Further, let's introduce some simple notation for use in the objective function and 24 constraints. Let: 25 = number of x-pods to be produced 26 X number of BlueBerrys to be produced Product Mix Question Scheduling Question H 1 J K Wichit shift LHS Decisi Sign RHS > > > A B D E F G x1 x2 X3 X4 X5 6 - Start to work at 3am 7am 11am 3pm 7pm 11pm 3 Work within Period 1 (3am - 7am) 5 Period 2 (7am - 11am) 6 Period 3 (11am - 3pm) 7 Period 4 (3pm - 7pm) 8 Period 5 (7pm - 11pm) 9 Period 6 (11pm - 3am) 10 11 Total # of Employees 12 13 Unit Costs (per hour/ per server) $ 20 $ 18 $ 16 $ 18 $ 20 $ 24 14 15 Total Cost 16 17 18 >= Owner required 19 20 21 22 23 Produit Mix Ouestion Scheduling Question K L M N P R S T U V Wichita's famous Seth Restaurant is open 24 hours a day. Servers report for duty at 3 AM 7AM. 11 AM 3PM 7PM or 11 PM, and each works an 8-hour shit. The following table shows the minimum number of workers needed during the 6 periods into which the day is divided Decision vairable X,= number of workers reporting for the start of working period i where i = 1,2,3,4,5, or 6 Period Time Number of Servers Required JAM-TAM 2 7 AM - 11 AM 14 3 11 AM - 3 PM 15 3 PM - 7PM 10 7 PM - 11 PM 12 11 PM -3 AM 5 Ownet Avandi Sethi's scheduling problem is to determine how many servers should report for work at the start of each time period in order to minimize the total stat required for one day's operation (Hint: Let X, equal the number of servers beginning work in time period where 1.2.3.4,5,6) 1 4 4 5 Scheduling Question 1111Z