(4) A manufacturing company produces products 1, 2, and 3. The three products have the following resourcerequirements and produce the following profit:Labor (hr/unit)5Material (Ib/unit)Profit ($/unit)Product142242At present, the firm has a daily labor capacity of 240 available hours and a daily supply of 400 pounds ofmaterial. The general linear programming formulation for this problem is as follows:Maximize Z = 3x, + 5x, + 2x3Subject to5x1 + 2x2 + 4x3 < 2404x1 + 6x2 + 3x3 5 400X1, X2, X3 2 0Management has developed the following set of goals, arranged in order of their importance to the firm: a. Because of recent labor relations difficulties, management wants to avoid underutilization of normalproduction capacity.b. Management has established a satisfactory profit level of $500 per day.c. Overtime is to be minimized as much as possible.d. Management wants to minimize the purchase of additional materials to avoid handling and storageproblems.Formulate a goal programming model to determine the number of each product to produce to best satisfythe goals.

Given data: Products and resource requirements Labour capacity = 240 hours Daily supply = 400 pounds…

Answered: A manufacturing company produces…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

See similar textbooks

Similar questions

Consider the following optimization problem: “Consider the ellipse given by . If you inscribe a rectangle in this ellipse, what are the dimensions of the rectangle that maximize its area? What is the maximum area?” Without actually solving the problem, detail the steps you would take if you were asked to solve the problem (say on an exam or homework). In other words, walk through the problem so you demonstrate an understanding of how you would go about finding the dimensions of the rectangle that maximize its area and the maximum area.
A scientist solves a nonhomogencous System of 10 linear equations in 12 unknowns and finds that three of the unknowns are free variables. Can the scientist be certain that, if the right sides of the equations are changed, the new homogencous system will have a solution ? To get the answer for above question, answer the followings (a) What is the order of the coefficient matrix? (b) ColA is a subspace of the vector space (c) What is dim Nul A ? (d) Write down the rank theorem. (e) What is rank A ? (f) What is dimCoIA ? (g) What is the conclusion for scientist's problem.
A linear programming computer package is needed. Edwards Manufacturing Company purchases two component parts from three different suppliers. The suppliers have limited capacity, and no one supplier can meet all the company's needs. In addition, the suppliers charge different prices for the components. Component price data (in price per unit) are as follows. Component Supplier 1 2 3 1 $13 $14 $15 2 $11 $12 $11 Each supplier has a limited capacity in terms of the total number of components it can supply. However, as long as Edwards provides sufficient advance orders, each supplier can devote its capacity to component 1, component 2, or any combination of the two components, if the total number of units ordered is within its capacity. Supplier capacities are as follows. Supplier 1 2 3 Capacity 500 900 700 If the Edwards production plan for the next period includes 900 units of component 1 and 700 units of component 2, what purchases do you recommend? That is, how many…
A company that operated 10 hours a day manufactures two products on three sequential processes. The following table summarizes the data for the problem: Product Process 1 10 Process 2 20 Process 3 8 10 Unit Profit 20 30 Which of the following is the most appropriate representation for variables x and y for the given situation? x is the # of units of Product 1 to be procured; y is the # of units of Product 2 to be procured. x is the # of units of Product 1 to be stored; y is the # of units of Product 2 to be stored x is the # of units of Product 1 to be delivered, y is the # of units of Product 2 to be delivered. x is the # of units of Product 1 to be produced; y is the # of units of Product 2 to be produced. minutes
The Perth Mining Company operates two mines for the purpose of extracting gold and silver. The Saddle Mine costs $14,000/day to operate, and it yields 50 oz of gold and 3,000 oz of silver per day. The Horseshoe Mine costs $16,000/day to operate, and it yields 75 oz of gold and 1,000 oz of silver per day. Company management has set a target of at least 650 oz of gold and 18,000 oz of silver. You boss would like you to focus on the following five issues: 1. How many days should each mine be operated so that the target can be met at a minimum cost? 2. Find the range of values that the Saddle Mine's daily operating cost can assume without changing the optimal solution. 3. Find the range of values that the requirement for gold and silver can assume. 4. Find the shadow price for the requirement for gold and silver.
Heller Manufacturing has two production facilities that manufacture baseball gloves. Production costs at the two facilities differ because of varying labor rates, local property taxes, type of equipment, capacity, and so on. The Dayton plant has weekly costs that can be expressed as a function of the number of gloves produced TCD(X) = x² - X + 9 where X is the weekly production volume in thousands of units and TCD(X) is the cost in thousands of dollars. The Hamilton plant's weekly production costs are given by TCH(Y) = y² + 2Y + 6 where Y is the weekly production volume in thousands of units and TCH(Y) is the cost in thousands of dollars. Heller Manufacturing would like to produce 9,000 gloves per week at the lowest possible cost. (a) Formulate a mathematical model that can be used to determine the optimal number of gloves to produce each week at each facility. X²-X+9+²+2Y+6 min s.t. X+Y X, Y 20 = 9 (b) Use Excel Solver or LINGO to find the solution to your mathematical model to…
Find the optimal solution for the following problem. (Round your answers to 3 decimal places.) Minimize C = 10x + 6y + 9z subject to 9x + 11y + 18z ≥ 69 12x + 14y + 4z ≥ 138 and x ≥ 0, y ≥ 0. a- What is the optimal value of x? b-What is the optimal value of y? c- What is the optimal value of z? d- What is the minimum value of the objective function?
I need help with this !
A linear programming computer package is needed. Frandec Company manufactures, assembles, and rebuilds material-handling equipment used in warehouses and distribution centers. One product, called a Liftmaster, is assembled from four components: a frame, a motor, two supports, and a metal strap. Frandec's production schedule calls for 4,500 Liftmasters to be made next month. Frandec purchases the motors from an outside supplier, but the frames, supports, and straps may be either manufactured by the company or purchased from an outside supplier. Manufacturing and purchase costs per unit are shown. Component Manufacturing Cost Purchase Cost Frame Support Min Strap Component Frame Support $37.00 Strap $10.50 Three departments are involved in the production of these components. The time (in minutes per unit) required to process each component in each department and the available capacity (in hours) for the three departments are as follows. $5.50 Cutting 3.5 1.3 0.8 Department 350 2.2 $50.00…
A transport company engaged in carying parcels has three branches to serve five customers. This distance (km) from each branch to each of the customers is given below: Branches Customers Number of C trucks available I 10 12 6. 15 II 4. 4. 6. 6. 7. 12 III 15 7. 11 13 8. 16 Number of 4. 6. trucks required i. Find out using Vogel's Approximation Method (VAM) the allocation of trucks from branches to customers in order to minimize the total cost of transportation assuming that the cost is proportional to distance. What is the minimum required distance (km) to be run by the trucks? i. If an amival of a V.V.I.P. blocks the traffic from branch II to customers D and E, what should be the optimal allocation in order to minimize the total transportation cost? 111. 8.
Please show your math! Steel Mills in three cities produce the following amounts of steels: Location Weekly Production (tons) A. Bethlehem 150 B. Birmingham 210 C. Gary 260 Total 620 These Mills supply steel to four cities, where manufacturing plants have the following demand: Location Weekly Demand (tons) 1. Detroit 130 2. St. Louis 70 3. Chicago 180 4. Norfolk 240 Total 620 Shipping Costs per ton of steel are as follows: To (Cost) 3. Chicago Form 1. Detroit 2. St. Louis 4. Norfolk A. Bethlehem $14 $9 $16 $18 B. Birmingham $11 $8 $7 $16 C. Gary $16 $12 $10 $22 a. Write down the function for Total cost in cell B19. b. Find the Minimum cost in cell B19 using Solver in Excel.
The Ace Manufacturing Company has orders for three similar products: Product Order (Units) A 1750 B 500 C 1100 Three machines are available for the manufacturing operations. All three machines can produce all the products at the same production rate. However, due to varying defect percentages of each product on each machine, the unit costs of the products vary depending on the machine used. Machine capacities for the next week and the unit costs are as follows: Machine Capacity (Units) 1 1550 2 1450 3 1150 Product Machine A B C 1 $0.80 $1.30 $0.70 2 $1.40 $1.30 $1.50 3 $0.80 $0.80 $1.20 Use the transportation model to develop the minimum cost production schedule for the products and machines. Show the linear programming formulation. If the constant is "1" it must be entered in the box. If your answer is zero enter "0". The linear programming formulation and optimal solution are shown. Let xij = Units of product j on machine i.…

SEE MORE QUESTIONS

Recommended textbooks for you

Practical Management Science

Operations Management

ISBN:

9781337406659

Author:

WINSTON, Wayne L.

Publisher:

Cengage,

Operations Management

ISBN:

9781259667473

Author:

William J Stevenson

Publisher:

McGraw-Hill Education

Operations and Supply Chain Management (Mcgraw-hi…

Operations Management

ISBN:

9781259666100

Author:

F. Robert Jacobs, Richard B Chase

Publisher:

McGraw-Hill Education

Practical Management Science

Operations Management

ISBN:

9781337406659

Author:

WINSTON, Wayne L.

Publisher:

Cengage,

Operations Management

ISBN:

9781259667473

Author:

William J Stevenson

Publisher:

McGraw-Hill Education

Operations and Supply Chain Management (Mcgraw-hi…

Operations Management

ISBN:

9781259666100

Author:

F. Robert Jacobs, Richard B Chase

Publisher:

McGraw-Hill Education

Business in Action

Operations Management

ISBN:

9780135198100

Author:

BOVEE

Publisher:

PEARSON CO

Purchasing and Supply Chain Management

Operations Management

ISBN:

9781285869681

Author:

Robert M. Monczka, Robert B. Handfield, Larry C. Giunipero, James L. Patterson

Publisher:

Cengage Learning

Production and Operations Analysis, Seventh Editi…

Operations Management

ISBN:

9781478623069

Author:

Steven Nahmias, Tava Lennon Olsen

Publisher:

Waveland Press, Inc.

SEE MORE TEXTBOOKS