A company produces three types of pencil holders: basic, deluxe, and supreme. All types require plastic, rubber, and silver as shown below:ТуреPlastic RubberSilverBasic122DeluxeSupreme224124The company has 700 units of plastic, 1000 units of rubber, and 1600 units of silver. It makes a profit of $5, $6, and $3 respectively on basic, deluxe, andsupreme pencil holders. Assuming that all pencil holders which are manufactured can be sold, determine the number of each type of pencil holder thecompany should produce to maximize its profit.Number of Basic pencil holders =Number of Deluxe pencil holders:=Number of Supreme pencil holders =

Let's examine the issue in greater detail. Pencil holder varieties made by the company are basic,…

Answered: A company produces three types of…

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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B. A firm manufactures 2 product, A and B. Each product is processed by machines, M₁ and M2. Each unit of type A requires 1 hour of processing by M₁ and 2 hours in M and each unit type of type B requires 3 hours on M₁ and 1 hour on M₂. The profit on product A is P20 per unit and on product B is P30 per unit. If M₁ is available for 200 hours each month and M₂ for 300 hours, how many units of each type can be manufactured in one month in order to maximize the profits? Requirement: 1) Formulate the linear programming model 2) Solve the linear programming using the graphical method
Suppose a certain manufacturing company produces connecting rods for 4- and 6-cylinder automobile engines using the same production line. The cost required to set up the production line to produce the 4-cylinder connecting rods is $2,400, and the cost required to set up the production line for the 6-cylinder connecting rods is $3,600. Manufacturing costs are $14 for each 4-cylinder connecting rod and $19 for each 6-cylinder connecting rod. Hawkins makes a decision at the end of each week as to which product will be manufactured the following week. If a production changeover is necessary from one week to the next, the weekend is used to reconfigure the production line. Once the line has been set up, the weekly production capacities are 5,000 6-cylinder connecting rods and 7,000 4-cylinder connecting rods. Let 56 = 1 if the production line is set up to produce the 6-cylinder connecting rods; 0 if otherwise (a) Using the decision variables x4 and s, write a constraint that limits next…
Tim Smunt has been asked to evaluate two machines. After some investigation, he determines that they have the costs shown in the following table: He is told to assume that: 1. The life of each machine is 3 years. Machine A Machine B Original Cost Labor per year $15,000 $20,000 $2,200 $4,000 Maintenance per year Salvage value $4,600 $1,000 $2,400 $7,500 2. The company thinks it knows how to make 8% on investments no more risky than this one. 3. Labor and maintenance are paid at the end of the year. • The NPV for Machine A: The NPV for Machine B: Using the net present value as the basis of comparing the machines, Tim should recommend:
Tim Smunt has been asked to evaluate two machines. After some investigation, he determines that they have the costs shown in the following table: Machine A Machine B Original Cost $12,000 $20,000 Labor per year $2,400 $4,400 Maintenance per year $4,000 $1,200 Salvage value $1,600 $7,500 He is told to assume that: 1. The life of each machine is 33 years. 2. The company thinks it knows how to make 88% on investments no more risky than this one. 3. Labor and maintenance are paid at the end of the year. 1. What is the NPV Value of Machine A? 2. Calculate the NPV for Machine B 3. Using the net present value as the basis of comparing the machines, Tim should recommend Machine A or B?
f. A drapper is required to supply two types of shirts type A and type B. The total number of shirts must not be more than 400. He has to supply more of type A than type B. However, the number of type A must not be more than 300 and the number of type B shirts must not be less than 80. Let x be the number of type A shirts and y be the number of type B shirts. If the profits were as follows: Type A Ksh 600 per shirt Type B Ksh 400 per shirt. Formulate a Linear Optimization Model, hence use the graphical method to determine the number of shirts of each type that should be made to maximize the profit.
Suppose a certain manufacturing company produces connecting rods for 4- and 6-cylinder automobile engines using the same production line. The cost required to set up the production line to produce the 4-cylinder connecting rods is $2,500, and the cost required to set up the production line for the 6-cylinder connecting rods is $3,900. Manufacturing costs are $13 for each 4-cylinder connecting rod and $16 for each 6-cylinder connecting rod. Hawkins makes a decision at the end of each week as to which product will be manufactured the following week. If a production changeover is necessary from one week to the next, the weekend is used to reconfigure the production line. Once the line has been set up, the weekly production capacities are 6,000 6-cylinder connecting rods and 8,000 4-cylinder connecting rods. Let x4 = the number of 4-cylinder connecting rods produced next week x6 = the number of 6-cylinder connecting rods produced next week s4 = 1 if the production line is set up to…
A company manufactures Products A, B, and C. Each product is processed in three departments: I, II, and III. The total available labor-hours per week for Departments I, II, and III are 780, 960, and 720, respectively. The time requirements (in hours per unit) and the profit per unit for each product are as follows. Dept. I Dept. II Dept. II Profit 144 Product A 240 2 3 2 $18 X Product B If management decides that the number of units of Product B manufactured must equal or exceed the number of units of products A and C manufactured, how many units of each product should the company produce to maximize its profit? product A 0 product B product C 1 1 2 $12 What is the maximum profit (in dollars)? $ 7038 X Product C 2 2 1 $15

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