LP MODEL FORMULATION1. RDB Manufacturing Company needs to provide capacity for manufacturing 10,750 units/month ofa new product for which it has won a contract. It has identified two machines that meet itsrequirements. Information on the machines and their availability is as follows:MachineMachine AMachine BCost/Machine$150,000$200,000Capacity,Parts/Month12501900Floor Space Needed,Square Feet/Machine3545MachineAvailableThe plant has a maximum of 300 square feet of space available for available for the additionalequipment. How many of each machine should the company purchase in order to support thecontract requirements at minimum equipment cost?

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Answered: LP MODEL FORMULATION 1. RDB…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Tattle Tots makes a fiberglass tricycle for kids that is composed of three major components: a handlebar-front wheel- pedal assembly, a seat, and frame unit, and rear wheels. The company has orders for 12,000 of these tricycles. The company does not have the resources available to manufacture everything needed for the completion of 12,000 tricycles so it has gathered purchase information for each component. The following table shows relevant information: Requirements Cost to Cost to Manufacture Purchase Component Plastic Time Space Front 3 10 2 12 Seat/Frame 4 2 6 9. Rear-wheel (each) .5 2 .1 1 3 Available 50,000 160,000 30,000 Develop a linear programming model to advise the operations manager of Tattle Tots how many of each component should be manufactured and how many should be purchased in order to provide 12,000 fully completed tricycles at the minimum cost. What is your best recommendation?
A contractor is planning a job that will require a large amount of gravel and sand. The estimates for the necessary gravel and sand are: Coarse gravel Fine gravel Sand 20,000 yd³ 29,000 yd³ 20,000 yd³ There are two pits from which material can be obtained, and the plan is to haul from these two pits and to separate (screen) on the job whatever material is needed. Analysis shows that the material at each pit has the following composition: Pit A Pit B Coarse gravel Fine gravel Sand Waste 20% 14% 25% 41% 30% 50% 20% 0% It costs $8/yd³ for material and hauling from pit A and $16/yd³ from pit B. Set this up as a linear programming problem to minimize delivered cost. Formulate and Solve with graphical solution method AND with Excel (Provide Model, Answer and Sensitivity Report)
17. A landscape gardener wants to build an 8000-square foot rectangular display garden along the side of a river. The garden will be fenced on three sides. (No fence is necessary along the river). She plans to use ornamental steel fencing at $12 per foot on the side opposite to river and chain-link fencing at $3 per foot on the other two sides. What dimensions for the garden will minimize her costs?
The Sentry Lock Corporation sells a variety of electronic goods through television shows. The company has a number of storages to keep the goods it sells, but also takes out a lease on additional storage space when required. During the next 5 months the company anticipates that it is going to need to take out a lease on the following amounts of additional storage space: Month 1 2 3 4 5 Square Feet(ft2) Needed 20,000 30,000 40,000 35,000 50,000 In the beginning of any month the company can take out a lease on additional space for one or more months at the following costs: Lease Term (months) 1 2 3 4 5 Cost per Sq. Ft. Leased $55 $85 $130 $165 $185 Therefore, for example, in the beginning of month 1 the company can take out a lease on as much space as it requires for four months at a cost of $165 per ft2 . Similarly, in the beginning of month 3 it can take out a lease on any amount of space for two months at a cost of $85 per ft2 . The company needs to determine the optimal way of…
Ensure to show your steps of calculations, formula and provide clear explanations for each part of the problem.
The Megabuck Hospital Corp. is to build a state-subsidized nursing home catering to homeless patients as well as high-income patients. State regulations require that every subsidized nursing home must house a minimum of 760 homeless patients and no more than 800 high-income patients in order to qualify for state subsidies. The overall capacity of the hospital is to be 2,100 patients. The board of directors, under pressure from a neighborhood group, insists that the number of homeless patients should not exceed twice the number of high-income patients. Due to the state subsidy, the hospital will make an average profit of $9,800 per month for every homeless patient it houses, whereas the profit per high-income patient is estimated at $7,800 per month. How many of each type of patient should it house in order to maximize profit? (If an answer does not exist, enter DNE.) high-income patients homeless patients profit
Joe Henry’s machine shop uses 2,500 brackets during the course of a year. These brackets are purchased from a supplier 90 miles away. The following information is known about the brackets: Annual demand: 2,500 Holding cost per bracket per year: $1.50 Order cost per order: $18.75 Lead time: 2 days Working days per year: 250 a) Given the above information, what would be the economic order quantity (EOQ)? b) Given the EOQ, what would be the average inventory? What would be the annual inventory holding cost? c) Given the EOQ, how many orders would be made each year? What would be the annual order cost? d) Given the EOQ, what is the total annual cost of managing the inventory? e) What is the time between orders? f ) What is the reorder point (ROP)?
As the production planner for Xiangling Hu Products, Inc., you have been given a bill of material for a bracket that is made up of a base, 1 spring, and 4 clamps. The base is assembled from 1 clamp and 2 housings. Each clamp has 1 handle and 2 castings. Each housing has 2 bearings and 1 shaft. There is no inventory on hand. a) Design a product structure noting the quantities for each item and show the low-level coding. Match each number in the structure below with the corresponding item. Number Item I Spring Subscript left parenthesis 1 right parenthesisSpring(1) II Housing Subscript left parenthesis 2 right parenthesisHousing(2) III Casting Subscript left parenthesis 2 right parenthesisCasting(2) IV Shaft Subscript left parenthesis 1 right parenthesisShaft(1) A rectangle at the top center is labeled Bracket. Three branches originate from this rectangle connect the rectangle to three rectangles. The…
A company is producing 3 products A ,B and C. BOM of each product is given in the table below. Material Unit Product A Product B Product C Steel Ton 4 Aluminum KG 50 40 60 Wood CFT 10 10 Glass SFT 30 30 Rubber Sealer RFT 100 120 Screws Рack 5 6 4 Nut Bolt Dozen 2 Calculate the material requirements for 6 months production for all the products if monthly demand for A=1000, B=1200 and C=1500 units
A pet food factory blends four ingredients into three types of pet food: value, premium, and basic. The maximum quantities available of each ingredient and the costs per ounce are given in the table below: Ingredient Maximum pounds available per day Cost per ounce 5,000 $0.5625 2 2,400 $0.4375 3 4,000 $0.7500 4 1,500 $0.3750 The operations manager has placed limits on the component to be added to each blend. The limits and the selling price for each blend are shown in the table below: Variant Component Specifications Selling Price per pound Value Not less than 40% of 1 $12.00 Value Not more than 20% of 2 $12.00 Value Not less than 30% of 3 $12.00 Premium Not less than 40% of 3 $18.00 Basic Not more than 50% of 2 $10.00 Basic Not less than 10% of 1 $10.00 The marketing manager wants to produce at least 3,000 pounds of each variant of pet food. Develop a linear programming model to help the company determine the best mix to produce to maximize profits. Determine the optimal solution and…
Terra Mesa Manufacturing uses a job order cost system to account for its production of specialty patio furniture. At the beginning of June, Terra Mesa had one job in Work in Process, job A75. Management has chosen direct labor cost as its activity base. The costs incurred to date on job A75 are as follows: Direct materials $8260 Direct labor 10500 Overhead 13125 During June, Terra Mesa added the following costs for direct materials and direct labor to job A75: Direct materials $2630 Direct labor 4620 Job A75 was competed on June 30. What is the cost of job A75? $26010 $39135 $44910 $42831
Describe the bounds, limitations, requirements, proportional relationships, and balance constraints: Young Energy operates a power plant that includes a coal-fired boiler to produce steam to drive a generator. The company can purchase different types of coals and blend them to meet the requirements for burning in the boiler. The following table shows the characteristics of the different types of coals: The required BTU/pound must be at least 11,900. In addition, the ash content can be at most 12.2% and the moisture content, at most 9.4%. Develop and solve a linear optimization model to find the best coal blend for Young Energy.

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