A factory manufactures three products, A, B, and C. Each product requires the use of two machines, Machine I and Machine II. The total hours available, respectively, on Machine I and Machine II per month are 5,540 and 10,350. The time requirements and profit per unit for each product are listed below.| | A | B | C ||-------|----|----|----|| Machine I | 4 | 7 | 8 || Machine II | 9 | 10 | 16 || Profit | $8 | $12| $18|**Problem Statement:**How many units of each product should be manufactured to maximize profit, and what is the maximum profit?Set up the linear programming problem, with A, B, and C representing the number of units of each product that are produced.**Objective Function:**Maximize $ P = $ **Constraints:**- $ 4A + 7B + 8C \leq 5,540 $- $ 9A + 10B + 16C \leq 10,350 $

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Answered: A factory manufactures three products,…

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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There are three factories located at AR, IN, and TX respectively. From these locations, a certain commodity is to be delivered to each of the two warehouses situated at A and B. The revenue per commodity item is $10. The weekly demand of the warehouse A and B are respectively 50 and 35 units of the commodity while the production capacity of the factories at AR, IN, and TX are respectively 28, 22, and 35 units. The cost of transportation per unit is given as belows. Cost Warehouse A Warehouse B AR 5 3 IN 6 6 TX 2 4 To maintain a good relationship with all the factories, warehouse B requires that it receives at least 40% of its product from factory in TX. Realize that it is making good profit in warehouse A, AR requires that at least 35% of its product shipped to warehouse A. Formulate (without solving) a linear programming problem to maximize the profit.
part a and b
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Production Line Speed and Quality Control. Brawdy Plastics, Inc., produces plastic seat belt retainers for General Motors at the Brawdy Plastics plant in Buffalo, New York. After final assembly and painting, the parts are placed on a conveyor belt that moves the parts past a final inspection station. How fast the parts move past the final inspection station depends upon the line speed of the conveyor belt (feet per minute. Although faster line speeds are desirable, management is concerned that increasing the line speed too much may not provide enough time for inspectors to identify which parts are actually defective. To test this theory, Brawdy Plastics conducted an experiment in which the same batch of parts, with a known number of defective parts, was inspected using a variety of line speeds. The following data were collected. a Develop a scatter diagram with the line speed as the independent variable. b) What does the scatter diagram developed in part (a) indicate about the…
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A factory manufactures three products, A, B, and C. Each product requires the use of two machines, Machine I and Machine II. The total hours available, respectively, on Machine I and Machine Il per month are 7,760 and 10,080. The time requirements and profit per unit for each product are listed below. ABC Machine I 7 9 10 Machine II 8 10 16 $12 $16 $22 Profit How many units of each product should be manufactured to maximize profit, and what is the maximum profit? Start by setting up the linear programming problem, with A, B, and C representing the number of units of each product that are produced. Maximize P = subject to: <7,760 s 10,080 Enter the solution below. If needed round numbers of items to 1 decimal place and profit to 2 decimal places. The maximum profit is $ when the company produces: units of product A units of product B units of product c

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