Formulate a linear program for this problem. 2) A hydroelectric dam needs to schedule how much power to produce in each of the next 24 hours. The demand in megawatts (MW) in hour t = 1, ..., 24 is dị. The power plant must produce at least the demand for each hour, but can produce more at a cost of K dollars per excess MW. For engineering reasons (can't open/close waterways too fast), after hour 1 the production in any given hour must be within 10 MW of the previous hour's production. For example, producing 25 MW in hour 3 means in hour 4 we have to produce between 15 and 35 MW. Finally, the combined production over 24 hours cannot exceed the reservoir capacity R. Please note that d, K, R are parameters, i.e. known values.
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- At a small but growing airport, the local airline company is purchasing a new tractor for a tractor-trailer train to bring luggage to and from the airplanes. A new mechanized luggage system will be installed in 3 years, so the tractor will not be needed after that. However, because it will receive heavy use, so that the running and maintenance costs will increase rapidly as the tractor ages, it may still be more economical to replace the tractor after 1 or 2 years. The following table gives the total net discounted cost associated with purchasing a tractor (purchase price minus trade-in allowance, plus running and maintenance costs) at the end of year i and trading it in at the end of year j (where year O is now). i 012 1 $13,000 j 2 $28,000 $17,000 3 $48,000 $33,000 $20,000 The problem is to determine at what times (if any) the tractor should be replaced to minimize the total cost for the tractors over 3 years. (a) Formulate this problem as a minimum cost flow problem by showing the…At a small but growing airport, the local airline company is purchasing a new tractor for a tractor-trailer train to bring luggage to and from the airplanes. A new mechanized luggage system will be installed in 3 years, so the tractor will not be needed after that. However, because it will receive heavy use, so that the running and maintenance costs will increase rapidly as the tractor ages, it may still be more economical to replace the tractor after 1 or 2 years. The following table gives the total net discounted cost associated with purchasing a tractor (purchase price minus trade-in allowance, plus running and maintenance costs) at the end of year i and trading it in at the end of year j (where year O is now). i B 012 1 $13,000 j 2 $28,000 $17,000 3 $48,000 $33,000 $20,000 The problem is to determine at what times (if any) the tractor should be replaced to minimize the total cost for the tractors over 3 years. (a) Formulate this problem as a shortest-path problem by drawing a…1) An operator is used for loading and unloading of parts to automated machines. Loading time is 1 minute; unloading time is 2 minutes, machining time is 30 minutes, Operator travel time between the machines including the inspection time is 4 minutes. Cost of operator is C₁=40 TL/Hour, cost of a machine is C₂-200 TL/Hour. What is the cost per unit of production if optimum number of machines is assigned to the operator? (Note: Times are given in minutes and costs are per hour) a) 231 TL/unit b) 6930 TL/unit c) 115.5 TL/unit d) 240 TL/unit e) 132 TL/unit 2) An operator is used for loading and unloading of parts to automated machines. Loading time is 1 minute; unloading time is 2 minutes, machining time is 30 minutes; Operator travel time between the machines including the inspection time is 4 minutes. Cost of operator is C1=40 TL/Hour; cost of a machine is C₂=200 TL/Hour. How many machines (integer number) should be assigned to the operator so that the total operator and machine costs…
- Chapter 5. (M/M/s/K Model). Leia is responsible for 8 computers in the IT offices in a small business called DataWish. Each computer runs on an average for 3 weeks and requires an average of ½ or 0.5 weeks to get reset by Leia before it can start up again. If we assign the Poisson distribution to the "arrival" of each computer for service and an exponential distribution to the actual service provided, answer the following questions: a. The arrival rate would be units per week and the service rate would be units per week. b. Calculate the following operating characteristics for the M/M/s/K system: Utilization Factor (p) % Performance Measures PO (probability that sytem is empty) L (average units in units system) La (average units waiting in queue) units W (average time in the weeks system) Wq (average time in the queue) weeks c. If we assign a cost of waiting as $500 per week per computer and $800 per week of hiring Leia, what is the Total Time Cost per week cost of servicing the…Chapter 5. (M/M/s/K Model). Leia is responsible for 8 computers in the IT offices in a small business called DataWish. Each computer runs on an average for 3 weeks and requires an average of ½ or 0.5 weeks to get reset by Leia before it can start up again. If we assign the Poisson distribution to the "arrival" of each computer for service and an exponential distribution to the actual service provided, answer the following questions: a. The arrival rate would bel units per week and the service rate would be units per week. b. Calculate the following operating characteristics for the M/M/s/K system: Utilization Factor (p) Performance Measures c. If we assign a cost of waiting as $500 per week per computer and $800 per week of hiring Leia, what is the Total Time Cost per week cost of servicing the machines? PO (probability that sytem is empty) % dollars L (average units in system) units d. If DataWish decides to hire another individual to help Leia, what would the new Total Time Cost per…Chapter 5. (M/M/s/K Model). Leia is responsible for 12 computers in the IT offices in a small business called DataWish. Each computer runs on an average for 4 weeks and requires an average of ½ or 0.5 weeks to get reset by Leia before it can start up again. If we assign the Poisson distribution to the “arrival” of each computer for service and an exponential distribution to the actual service provided, answer the following questions: a. The arrival rate would be units per week and the service rate would be units per week. b. Calculate the following operating characteristics for the M/M/s/K system: Utilization Factor (ρ) % Performance Measures P0 (probability that sytem is empty) % L (average units in system) units Lq (average units waiting in queue) units W (average time in the system) weeks Wq (average time in the queue) weeks c. If we assign a cost of waiting as $750 per week per computer and $800 per week of…
- Problem3: Optimizing Manufacturing Production Line Scenario: You are a manufacturing manager responsible for a production line that assembles and packages electronic devices. The goal is to optimize the production process to increase throughput, reduce cycle times, minimize bottlenecks, and ensure efficient resource utilization. Explain the steps to build simulation model using Arena.Solve the question below using the attached excel templates with formulas for renting both slow and fast copies (labeled in the excel tabs). Question: The Decision Sciences Department is trying to determine whether to rent a slow or a fast copier. The department believes that an employee’s time is worth $15 per hour. The slow copier rents for $4 per hour, and it takes an employee an average of 10 minutes to complete copying. The fast copier rents for $15 per hour, and it takes an employee an average of six minutes to complete copying. On average, four employees per hour need to use the copying machine. (Assume the copying times and interarrival times to the copying machine are exponentially distributed.) Which machine should the department rent to minimize expected total cost per hour?Given the following for a retail property: This property is occupied by a single tenant: Net Rentable Space 10,000 sq. ft. Lease Rate $18.00 per sq. ft. per year Real Estate Taxes $ 1.75 per sq. ft. per year Operating Expenses $ 0.55 per sq. ft. per year Insurance $ 0.06 per sq. Ii. per year Actual Gross Sales $2,200,000 Base Sales as per Lease $2,000,000 Percentage Lease Clause 4.0% What is the amount of rent due on a per sq. ft. basis (per year) ifthe tenant has a "net net"_ (NN)Jease and a "percentage lease clause" in the lease? Please provide proper keystrokes for the BAii Plus and Gualifier Plus IIIfx calculators. Thank you!
- ADVANCED ANALYSIS Linear equations for the consumption and saving schedules take the general form: C = a + bY and S = -a + (1-b)Y where C, S, and Y are consumption, saving, and national income, respectively. The constant a represents the vertical intercept, and b represents the slope of the consumption schedule. a. Use the following data to substitute specific numerical values into the consumption and saving equations. Instructions: If you are entering any negative numbers be sure to include a negative sign (-) in front of those numbers. C = $ Y. S = $ Y. b. What is the economic meaning of b? . What is the economic meaning of (1 – b)? .Design capacity is the ability of the company to produce the quantity of goods and services within a particular period of time when the company have best condition to produce and when the company have unlimited resources. These resource's includes- Men, Machinery, Material etc. It shows the maximum capacity of the company to produce. Effective capacity refers to the ability of the company to produce maximum quantity within a particular period of time to achieve in current production condition and current resources. It shows the real outcome capacity of the firm when the company produce within their own current condition of their production. Question Why is the capacity design important?Design capacity is the ability of the company to produce the quantity of goods and services within a particular period of time when the company have best condition to produce and when the company have unlimited resources. These resource's includes- Men, Machinery, Material etc. It shows the maximum capacity of the company to produce. Effective capacity refers to the ability of the company to produce maximum quantity within a particular period of time to achieve in current production condition and current resources. It shows the real outcome capacity of the firm when the company produce within their own current condition of their production. In design capacity it is assume that the company will produce in best and ideal condition to produce goods and services while in Effective capacity it is assume that company will produce in current operating conditions. In design capacity it is assume that the company have unlimited resource's. It means these resource's include:- Men,…