n a factory they have type A machines and type B machines. Last week maintenance was given to 5 type A machines and 4 type B machines at a cost of $3,405,000. The previous week, $3,135,000 was paid to maintain 3 type A machines and 5 type B machines. What is the maintenance cost of the machines of each type?
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- Green Vehicle Inc. manufactures electric cars and small delivery trucks. It has just opened a new factory where the C1 car and the T1 truck can both be manufactured. To make either vehicle, processing in the assembly shop and in the paint shop are required. It takes 1/40 of a day and 1/60 of a day to paint a truck of type T1 and a car of type C1 in the paint shop, respectively. It takes 1/50 of a day to assemble either type of vehicle in the assembly shop. A T1 truck and a C1 car yield profits of $300 and $220, respectively, per vehicle sold. a) Define the objective function and constraint equations. b) Graph the feasible region. c) What is a maximum-profit daily production plan at the new factory? d) How much profit will such a plan yield, assuming whatever is produced is sold?A furniture company is producing tables and chairs for the coming week. The production of tables and chairs will go through two processes: wood cutting and assembly. In the woodcutting process, the required labor hour is 1 hour for a chair and 2 hours for a table. In the assembly process, the required labor hour is 4 hours for a chair and 3 hours for a table. For the coming week, the maximum labor hour is 70 hours for the wood cutting process and 180 hours for the assembly process. Based on the company’s inventory level, the company decides to produce no more than 100 chairs and 30 tables for the coming week. Suppose the profit margin is $5/chair and $6/ table. Set up a linear programming model to maximize the total profit for this furniture company and solve the model using Excel Solver. A. What is the optimal solution? B. What are the values of the slack/surplus variables at the optimal solution?At a manufacturing assembly line, 30 jobs arrive perhour. Each job must pass through two production stages:stage 1 and stage 2. Stage 1 takes an average of 1 minute tocomplete, and 1 worker is available to perform stage 1.After completing stage 1, the job immediately passes tostage 2. Stage 2 takes an average of 2 minutes to complete,and 2 workers are available to work on stage 2. Aftercompleting stage 2, each job is inspected. Inspection takesan average of 3 minutes, and 3 workers are available toperform inspection. After inspection, 10% of the jobs mustbe returned to stage 1, and they then repeat both stages 1and 2. After inspection, 20% of all jobs return to stage 2 andrepeat stage 2. Assume that interarrival times and servicetimes are exponential.a What is the average time a job spends in the systemfrom arrival to completion?b What percentage of the time is each worker busy?
- Sunseel Industries produces two types of raw materials, A and B, with a production cost of $4 and $8 per unit, respectively. The combined production of A and B must be at least 700 units per month. The factory is expected to produce at least 400 units of B and not more than 1200 units of A each month. The processing times for A and B are observed to be 5 hours and 4 hours, respectively. A total of 3000 production hours are available per month. Develop a linear program that Sunseel Industries can use to determine the number of units of each raw material to produce that will meet the demand and minimize the total cost.green vehicule Inc. manufactures electric cars and small delivery trucks. it has just opened a new factory where the C1 car and the T1 truck can both be manufactured. to make either vehicle, processing in the assembly shop and the paint shop are required. It takes 1/40 of a day and 1/60 of a paint a truck of type T1 and a car of type C1 in the paint shop, respectively. it takes 1/50 of a day to assemble either type of vehicule in the assembly shop. A t1 truck and a C1 car yield profits of $300 and $220, respectively, per vehicule soldThe Toys-R-U Company has developed two new toys for possible inclusion in its product line for the upcoming Christmas season. Setting up the production facilities to begin production would cost $50,000 for toy1 and $80,000 for toy 2. Once these costs are covered, the toys would generate a unit profit of $10 for toy 1 and $15 for toy 2. The company has two factories that are capable of producing these toys. However, to avoid doubling the start-up costs, just one factory would be used, where the choice would be based on maximizing profit. For administrative reasons, the same factory would be used for both new toys if both are produced. Toy 1 can be produced at the rate of 50 per hour in factory 1 and 40 per hour in factory 2. Toy 2 can be produced at the rate of 40 per hour in factory 1 and 25 per hour in factory 2. Factory 1 and 2, respectively, have 500 hours and 700 hours of production time available before Christmas that could be used to produce these toys. It is not known…
- Vollmer Manufacturing makes three components for sale to refrigeration companies. The components are processed on two machines: a shaper and a grinder. The times (in minutes) required on each machine are as follows: Machine Component Shaper Grinder 1 6 4 2 4 5 3 4 2 The shaper is available for 120 hours, and the grinder is available for 110 hours. No more than 200 units of component 3 can be sold, but up to 800 units of each of the other components can be sold. In fact, the company already has orders for 600 units of component 1 that must be satisfied. The profit contributions for components 1, 2, and 3 are $8, $6, and $9, respectively. (a) Formulate and solve for the recommended production quantities. component 1 unitscomponent 2 unitscomponent 3 units (b) What are the objective coefficient ranges for the three components? (If there is no upper or lower limit, enter NO LIMIT. Round your answers to the nearest integer.) component 1 blank to blank units…Four automobiles have entered Ilham’s Repair Shop for various types of work, ranging from a transmission overhaul to a brake job. The experience level of the mechanics is quite varied, and Ilham would like to minimize the time required to complete all of the jobs. He has estimated the time in minutes for each mechanic to complete each job. Shima can complete job 1 in 400 minutes, job 2 in 90 minutes, job 3 in 60 minutes, and job 4 in 120 minutes. Dekmal will finish job 1 in 650 minutes, job 2 in 120 minutes, job 3 in 90 minutes, and job 4 in 180 minutes. Tia will finish job 1 in 480 minutes, job 2 in 120 minutes, job 3 in 80 minutes, and job 4 in 180 minutes. Hazza will complete job 1 in 500 minutes, job 2 in 110 minutes, job 3 in 90 minutes, and job 4 in 150 minutes. Each mechanic should be assigned to just one of these jobs. Draw the initial table for this assignment problem.Vollmer Manufacturing makes three components for sale to refrigeration companies. The components are processed on two machines: a shaper and a grinder. The times (in minutes) required on each machine are as follows: Machine Component Shaper Grinder 1 6 4 2 4 5 3 4 2 The shaper is available for 120 hours, and the grinder is available for 110 hours. No more than 200 units of component 3 can be sold, but up to 900 units of each of the other components can be sold. In fact, the company already has orders for 600 units of component 1 that must be satisfied. The profit contributions for components 1, 2, and 3 are $8, $6, and $9, respectively. (a) Formulate and solve for the recommended production quantities. component 1 unitscomponent 2 unitscomponent 3 units (b) What are the objective coefficient ranges for the three components? (If there is no upper or lower limit, enter NO LIMIT. Round your answers to the nearest integer.) component 1 to unitscomponent 2 to…
- Vollmer Manufacturing makes three components for sale to refrigeration companies. The components are processed on two machines: a shaper and a grinder. The times (in minutes) required on each machine are as follows: Machine Component Shaper Grinder 1 7 5 2 5 5 3 5 2 The shaper is available for 125 hours, and the grinder is available for 95 hours. No more than 170 units of component 3 can be sold, but up to 1050 units of each of the other components can be sold. In fact, the company already has orders for 625 units of component 1 that must be satisfied. The profit contributions for components 1, 2, and 3 are $8, $6, and $9, respectively. If more time could be made available on the grinder, how much would it be worth? If required, round your answers to two decimal places.$ _____ per minute, since the dual value is _____ on the grinder at the optimal solution.A project director runs a staff consisting of 6 scientists and 3 lab technicians. Three new projects have to be worked on and the director decides to assign 4 of her staff to the first project, 3 to the second, and 2 to the third. In how many ways can this be accomplished if each project requires 1 lab technician?A restaurant operates from 8 a.m. to 8 p.m. and employs both full-time and part-time workers. Full-time workers work from 8 a.m. to 6 p.m., 9 a.m. to 7 p.m., or 10 to 8 p.m. and are paid $140 per day. Part-time workers work either 12 p.m. to 6 p.m. or 1 p.m. to 7 p.m. and are paid $85 per day. The number of employees needed every hour is as follows. Develop a work schedule that minimizes daily labor costs. What is the optimal minimum cost? 8-9A 7 9-10A 8 10-11A 8 11A-12P 6 12-1P 7 1-2P 8 2-3P 10 3-4P 9 4-5P 9 5-6P 8 6-7P 3 7-8P 2