A manufacturing firm produces three products A, B, and C, each of which need to be processed in three departments, milling, grinding, and packaging. Each unit of Product A requires 4, 5, and 3 hours in each of the three departments. Likewise, Product B requires 8, 5, and 5 hours, while Product R requires 2, 5, and 6 hours in the three departments respectively. Every day (90+X), (105+X), and (150+X) hours are available in the three departments. The unit contribution of the products A, B, and C is Rs. 6, Rs. 12, and Rs. 8 respectively. Formulate the given problem as an LPP and find the solution.
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- During an eight-hour shift, 750 non-defective parts are desired as a result of a manufacturing operation. The default operation time is 15 minutes. As the operators of machine are inexperienced, the actual time they take to perform the operation is 20 minutes, and, on average, a fifth of the parts that start to be manufactured are lost. Assuming that each one of the machines used in this operation will not be available for one hour in each shift, determine the number of machines needed.A machine used for cutting materials in a factory has the following outputs per hour at various speeds and required periodic tool regrinding at intervals cited. Speed Hour Output per Tool RegrindingA 200 pieces every 8 hours B 280 pieces every 5 hours A set of tools costs 560 and can be ground twenty times. Each regrinding costs 54.00 and the time needed to regrind and change tools is 1 hour. The machine operator is paid 35.00 per hour including the time the tool is changed. The tool grinder who also sets the tools to the machine is paid 40.00 per hour. The hourly rate chargeable against the machine is 38.00, regardless of machine speed. Which speed is more ecomical? A. Speed B, 0.096/pc B Speed B, 0.087/pc C. Speed A, .054/pc D. Speed A >037/pcA diabetic patient needs at least 40 units of Vit. A, at least 30 units of Vit. C, and at least 40 units 30 units of Vit. E each day. Each brand X multivitamin capsule contains 4 units of Vit. A, 6 units of Vit. C, and 2 units of Vit. E; each brand Y capsule contains 5 units of Vit. A, 3 units of Vit.C, and 5 units of Vit. E. If each brand X capsule costs P6.00 and each brand Y capsule costs P9.00, how many capsules should the patient take each day to minimize the costs?
- There is an upstream Picking department that feeds two downstream Packing departments: Pack Singles and Pack Multis. Those Packing departments feed to a Shipping department that loads the outgoing trucks. 40% of your Pick volume goes to Pack Singles and has a packing rate of 104 units per labor hour (uph). 60% of the Pick volume goes to Pack Multis and has a pack rate of 215 units per labor hour. Your pickers pick both Single and Multi items throughout the day at an overall average rate of 114 units per labor hour. All units that are packed in both processes go through the Ship process at a rate of 570 units per hour. You have 102 people today for all 4 departments and you absolutely must pack 47,880 units in Pack Multis Items to meet a customer promise metric. How do you allocate labor to balance the flow in your department if you work a 10 hour shift? Do not assume breaks or lunches in your answer. Redirect 1: You now need to process all of the Pack Singles Volume in the first 5…A bank is trying to determine which of two machinesshould be rented to process checks. Machine 1 rents for$10,000 per year and processes 1,000 checks per hour.Machine 2 rents for $15,000 per year and processes 1,600checks per hour. Assume that the machines work 8 hours aday, 5 days a week, 50 weeks a year. The bank must processan average of 800 checks per hour, and the average checkprocessed is for $100. Assume an annual interest rate of20%. Then determine the cost to the bank (in lost interest)for each hour that a check spends waiting for and undergoingprocessing. Assuming that interarrival times and servicetimes are exponential, which machine should the bank rent?An injector machine goes down roughly 20% of the time (the injector gums up and needs to be cleaned, a quick process). One operator is assigned to service three identical such machines. Each machine can produce 100 parts/h if running properly (i.e., not down). The operator is paid $10/h and each machine costs $20/h to operate. Consider 8hr/shift a) Please fill in the table below: b) How many parts can you produce per shift? c) What is the unit cost fper part for this operation? d) If you hire another operator at the same rate to assist the first operator, what is the unit cost now? e) Is it worth hiring another operator at the same rate to assist the first operator, in case more than one machine goes down at the same time?
- Joan has a small design and tailoring shop making custom outfits for women. She has two employees. Each employee only begins working on a dress when a customer order has been received and then she makes the dress from beginning to end. The average production time of a dress is 1.8 days, with a standard deviation of 2.1 days. Historically, Joan has been receiving orders with interarrival times of one day on average. The interarrival times of orders have a coefficient of variation of one. (Carry at least 4 decimal places in all intermediate calculations. Round your final answer to 2 decimal places.) What is the expected waiting time, in days, between when an order is received and when production begins on the dress? A. 9.12 days B. 6.50 days C. 1.23 days D.3.41 days2. Frank Underwood is able to install new mufflers for his customers needing this service arrive at the shop. Frank Underwood uses three workers for his work, i.e., m=3. All the workers have same service rate. The hourly service rate of an individual worker and the hourly arrival rate of the gustomers can be obtained from the equation. x3 - x² – 69x +189 = 0. It is known that the hourly service rate of an individual worker is less than the hourly customer arrival rate. The process follows assumptions of M/M/m model. Now answer the following questions| a) What is the arrival rate of the customers (2) and service rate of an individual worker (H).2 (Clearly write down the equation in the form of factors before writing the final solutions) b) What is the probability of no customer in the system, i.e., (Pa)? c) What is the average number of customers in the queue (La) d) What is the average time a customer spends waiting in the queue (W (in hours)? e) What is the utilization rate (Q)A manufacturing plant produces a product 'A' that requires one unit of 'B' and ½ unit of 'C'. Each unit of 'B' is comprised of one unit of 'D', two units of 'E', and one unit of 'F'. Each unit of 'C' requires ½ unit of 'G' and three units of 'H'. The manufacturing lead times for the components are as follows: 'A' - two weeks, 'B' - one week, 'C' - two weeks, 'D' - two weeks, 'E' - three weeks, 'F' - one week, 'G' - two weeks, 'H' - one week. There are 20 units in stock for each of these components. 100 units of 'A' are needed for delivery in seven weeks: a) Develop the product structure and indexed bill of materials for the product. b) Create a gross and net requirements plan for the manufacturer of the product.
- A Company that makes shopping carts for supermarkets and other stores recently purchased some new equipment that reduces the labor content of the jobs needed to produce the shopping carts. Prior to buying the new equipment, the company used 4 workers, who produced an average of 87 carts per hour. Workers receive $13 per hour, and machine coast was $32 per hour. With the new equipment, it was possible to transfer one of the workers to another department, and equipment cost increased by $18 per hour while output increased by four carts per hour.a) Compute the multifactor productivity (MFP) (labor plus equipment) under the Prior to buying the new equipment. The MFP (carts/$) = ( ) (round to 4 decimal places).b) Compute the % growth in productivity between the Prior to and after buying the new equipment. The growth in productivity = ( ) % (round to 2 decimal places)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…A Company that makes shopping carts for supermarkets and other stores recently purchased some new equipment that reduces the labor content of the jobs needed to produce the shopping carts. Prior to buying the new equipment, the company used 7 workers, who produced an average of 87 carts per hour. Workers receive $15 per hour, and machine coast was $43 per hour. With the new equipment, it was possible to transfer one of the workers to another department, and equipment cost increased by $14 per hour while output increased by four carts per hour. a) Compute the multifactor productivity (MFP) (labor plus equipment) under the Prior to buying the new equipment. The MFP (carts/S) = Blank 1 (round to 4 decimal places). b) Compute the productivity changes between the Prior to and after buying the new equipment. The productivity growth = Blank 2% (round to 2 decimal places) Blank 1 Add your answer Blank 2 Add your answer