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For networks (1) and (2), find the maximal flow from the source to the sink, given that the flow capacity from node I to node j is the number along branch (ij) nearest node i.
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- The State U doctoral program in business admits anaverage of 25 doctoral students each year. If a doctoralstudent spends an average of 4 years in residence at StateU, how many doctoral students would one expect to findthere?A mom and pop car wash with 1 drive through lane gets an average of 4 cars per hour, with a Poisson distribution. The washing and drying process has a mean of 12 minutes, M= exponentially distributed, and a car cannot enter the lane until the car in front of it is finished drying (there can only be one car in the lane at one time). Due to the location, there is only space enough to hold 5 cars in line waiting to get washed. However, they rent space from the empty lot next door that is large enough to hold as many cars as needed. They decided to rent a section that will hold only 3 cars. a) If they decide to rent a section that will hold 3 cars, what will you solve for to determine the probability that they will still turn cars away? b) They promise each customer their money back ($10) if it takes longer than 30 minutes to get their car washed (from the time they enter). They are open 8 hours per day. How much money can they expect to give away per day?A city would like to know how many vehicles it could move through its streets in an emergency. The most likely situation is an evacuation starting at the school and ending at the park. The connections between these two locations, plus their capacity and direction, is shown below. School B Path Capacity Oak Street Elm Street A 10 с E B C 20 15 1 Street D 30 2nd Street E 25 F F 20 Park G 15
- Discuss how the principle of queues can be used when designing queueing schemes to reduce overall service costs?A city would like to know how many vehicles it could move through its streets in an emergency. The most likely situation is an evacuation starting at the school and ending at the park. The connections between these two locations, plus their capacity and direction, is shown below. School A B Path Capacity Oak Street Maximum Flow Elm Street с E 1* Street 2nd Street D E 30 20 A C F B 30 15 30 5 (Round your answer to the nearest whole number.) F G Park G 5The 4M company has a lathe as the centerpiece of the plant's work. The jobs arrive according to a Poisson process with an average rate of 2 per day. The processing time of each job is exponentially distributed with an average of 1/ 4 day. Since the jobs are large, if they are not in process they are stored in a warehouse some distance from the machine. However, to save time in bringing them in, the production manager proposes to add space for 3 in-process jobs in addition to the one on the lathe (the rest will continue to be stored). With this proposal, what proportion of the time will the space next to the lathe be adequate for the waiting jobs? Calculate your answer using the formulas available.
- A supplier ships goods from Richmond, VA to three market places in 3 cities (Chicago, IL; Athens, GA; St. Luis, MO). The supplier can ship every day, every other day, or every third day. There is a penalty of $0.30/cwt for each day delayed. Consolidating shipments allows for lower transportation costs from larger loads, but incurs penalty costs due to the delay. Transportation Rate (S/cwt) Shipment City Weight/day LTL 50,000 lb 50000 lb Chicago, IL 18,000 lb (180 cwt) 1.50 1.25 Athens, GA 15,000 lb (150 cwt) 1.35 1.00 St. Luis, MO 12,000 lb (120 cwt) 2.00 1.50 Total 45,000 Ib = 450 cwt Find what is the cost for the following: Shipping Every Day Shipping on the alternate Day (every two days) Shipping every three DayDefine and explain the perpetual mapping with help of example.Pickson Luthiers Corporation makes four models of electric guitars, ScarCT, Dela Mort, Warax, and Invazen. Each guitar must flow through five departments, assembly, painting, sound testing, inspection, and packaging. The accompanying table shows the relevant data. Production rates are shown in units/hour. (ScarCT is assembled elsewhere.) Pickson wants to determine how many guitars to make to maximize monthly profit. According to the linear optimization model, what would be the total time in hours spent on inspecting the Dela Mort models? Round to two decimal places. Click the icon to view the model. A. 12.50 B. 158.33 C. 85.00 D. 48.00 Production Model Pickson Luthiers Corporation Data Guitar Model ScarCT Dela Mort Warax Invazen Selling price/Unit Variable cost/Unit Min Sales Max Sales 750.00 660.00 0 2500 788.00 0 2000 680.00 700.00 800.00 1000 850.00 800.00 500 Production rates (units/hour) ScarCT Assembly Painting Sound Testing Inspection Packaging 35 20 10 9 Dela Mort 35 20 10 12…
- A supplier ships goods from Richmond, VA to three market places in 3 cities (Chicago, IL; Athens, GA; St. Luis, MO). The supplier can ship every day, every other day, or every third day. There is a penalty of $0.30/cwt for each day delayed. Consolidating shipments allows for lower transportation costs from larger loads, but incurs penalty costs due to the delay. Transportation Rate (S/cwt) Shipment City Weight/day LTL 50,000 lb 50000 lb Chicago, IL 18,000 lb (180 cwt) 1.50 1.25 Athens, GA 15,000 lb (150 cwt) 1.35 1.00 St. Luis, MO 12,000 lb (120 cwt) 2.00 1.50 Total 45,000 Ib = 450 cwt Find what is the cost for the following: Shipping Every Day Shipping on the alternate Day (every two days) Shipping every three DayA supplier ships goods from Richmond, VA to three market places in 3 cities (Chicago, IL; Athens, GA; St. Luis, MO). The supplier can ship every day, every other day, or every third day. There is a penalty of $0.30/cwt for each day delayed. Consolidating shipments allows for lower transportation costs from larger loads, but incurs penalty costs due to the delay. Transportation Rate (S/cwt) Shipment City Weight/day LTL 50,000 lb 50000 lb Chicago, IL 18,000 lb (180 cwt) 1.50 1.25 Athens, GA 15,000 lb (150 cwt) 1.35 1.00 St. Luis, MO 12,000 lb (120 cwt) 2.00 1.50 Total 45,000 Ib = 450 cwt Find what is the cost for the following: Shipping Every Day Shipping on the alternate Day (every two days) Shipping every three DayJohn is travelling from home in Sydney to a hotel in Perth. Three stopovers on the way a number of choices of towns for each stop only one hotel to choose from in each town, except for Perth, where there are three hotels (J, K, and L) to choose from Each trip has a different distance resulting in a different cost (petrol) (cost is marked by each arc) Hotels have different costs (cost is marked by each node (town)) ● ● ● The goal is to select a route to and a hotel in Perth so that the overall cost of the trip is minimized. Use dynamic programming (forward recursion) to solve this problem by constructing the usual tables for each stage. Stage: 0 (Sydney) 1 Petrol cost start 22 8 12 Hotel cost 70 80 B 80 25 10 2 50 A E 70 30 10 18 8 7 3 50 F 70 70 H 60 8 10 10 4 (Perth) 50 13 K 10 15 L 60 70