(2). A company produces tables at its two factories A and B. The next three months, the company mustprovide its customers (on time!) the following: 300 tables in month 1, 400 tables in month 2 and 500 in month3. A table produced in factory A requires 1.5 hours of skilled labour. A table produced at factory B requires2 hours. It costs $40 to produce a table in factory A and $35 at factory B. During each month, each factoryhas 600 hours of skilled labour. It costs $10 to hold a table in inventory for one month. Formulate an LPwhose solution will tell the company how to minimize the cost of meeting demand for the next three months.Make sure to clearly define your variables!

Month Demand 1 300 2 400 3 500 The cost details: Labor hours Cost Factory A 1.5 hrs…

Answered: (2). A company produces tables at its…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter4: Linear Programming Models

Section: Chapter Questions

Problem 59P

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22, A small generator burns two types of fuel low sulfur and high sulfur to produce electricity. For one hour, each gallon of low sulfur emits 3 units of sulfur dioxide, generates 4 kilowatts of electricity and costs P200. Each gallon of high sulfur emits 5 units of sulfur dioxide, generates 4 kilowatts and costs P220. The Environmental Protection Agency insists that the maximum amount of sulfur dioxide that can be emitted per hour is 15 units. Suppose at least 16 kilowatts must be generated per hour, what is the appropriate objective function if the company would like to have the most economical mix? Let x be the number of units of low sulfur fuel and y be the number of high sulfur fuel.
2. A craftsman named William Barnes builds two kinds of birdhouses, one for wrens and a second for bluebirds. Each wren birdhouse takes 4 hours of labor and 4 units of lumber. Each bluebird house requires 2 hours of labor and 12 units of lumber. The craftsman has available 48 hours of labor and 120 units of lumber. Wren houses yield a profit of $10 each and bluebird houses yield a profit of $15 each. 1. The aim of the objective function for William should be to _______ a. Maximize b. Minimize the objective value. 2. a. Write out the objective and constraints. b. Solve graphically
Kelson Sporting Equipment, Inc., makes two different types of baseball gloves: a regular model and a catcher's model. Letting R = number of regular gloves C = number of catcher's mitts leads to the following formulation: Max 6R + 9C s.t. R + 3 2 C ≤ 1,000 Cutting and sewing 1 2 R + 1 3 C ≤ 300 Finishing 1 8 R + 1 4 C ≤ 100 Packaging and shipping R, C ≥ 0 The computer solution is shown below. Optimal Objective Value = 4350.00000 Variable Value Reduced Cost R 500.00000 0.00000 C 150.00000 0.00000 Constraint Slack/Surplus Dual Value 1 275.00000 0.00000 2 0.00000 4.50000 3 0.00000 30.00000 Variable ObjectiveCoefficient AllowableIncrease AllowableDecrease R 6.00000 7.50000 1.50000 C 9.00000 3.00000 5.00000 Constraint RHSValue AllowableIncrease AllowableDecrease 1 1000.00000 Infinite 275.00000 2 300.00000 100.00000 166.66667 3…
2 ABCD company is an office equipment company that produces two types of desks: standard and deluxe. Deluxe desks have oak tops, more expensive hardware, and require additional time for finishing and polishing. Standard desks require 80 square feet of pine and 10 hours of labor, while deluxe desks require 60 square feet of pine, 18 square feet of oak, and 16 hours of labor. For the next week, the company has 5,000 square feet of pine, 750 square feet of oak, and 400 hours of labor available. Standard desks net a profit of $150, while deluxe desks net a profit of $320. All desks can be sold to national chains shops. Instructions: If the spreadsheet and Excel Solver results are given to you as follows (see Table 1 below), address the following questions: What are your Binding Constraints? What is your Optimum profit [hint: maximized profit]? What are your slack values for Pine, Oak, and Labor? Looking at the Shadow prices, how much would the objective profit increase by if you were to…
Kelson Sporting Equipment, Inc., makes two different types of baseball gloves: a regular model and a catcher's model. Letting R = number of regular gloves C = number of catcher's mitts leads to the following formulation: Max 5R + 8C s.t. R + 3 2 C ≤ 800 Cutting and sewing 1 2 R + 1 3 C ≤ 280 Finishing 1 8 R + 1 4 C ≤ 100 Packaging and shipping R, C ≥ 0 The computer solution is shown below. Optimal Objective Value = 3640.00000 Variable Value Reduced Cost R 440.00000 0.00000 C 180.00000 0.00000 Constraint Slack/Surplus Dual Value 1 90.00000 0.00000 2 0.00000 3.00000 3 0.00000 28.00000 Variable ObjectiveCoefficient AllowableIncrease AllowableDecrease R 5.00000 7.00000 1.00000 C 8.00000 2.00000 4.66667 Constraint RHSValue AllowableIncrease AllowableDecrease 1 800.00000 Infinite 90.00000 2 280.00000 120.00000 146.66667 3 100.00000 18.00000 30.00000 (a) Determine the objective coefficient ranges. (Round your answers to two decimal places.)…
Example 1. The Big M Method solve LP with mixed constraints Minimize: Z = 4x1 + 2x2 + x3 Subject to: 2x1 + 3x2 + 4x3 ≤ 14 3x1 + x2 + 5x3 ≥ 4 x1 + 4x2 + 3x3 ≥ 6 x1, x2, x3≥ 0
Suppose an assignment problem, where there are 3 employees who must perform 3 different tasks. The times (in hours) that employees take to perform each of the tasks is shown below. Each employee must perform only one task, and a task can only be performed by one employee. All employees are paid exactly the same wage per hour of work. Minimize the total time to make all tasks. Task 1 Task 2 Task 3 Employee 1 154 29 40 Employee 2 18 137 12 Employee 3 94 13 31 How many variables does the problem have? How many constraints does the problem have? The objective function corresponds to:
INCORRECT FORFormulate a linear programming model that can be used to determine the pounds of Brazilian Natural and Colombian Mild that will maximize the total contribution to profit. (Let BR = pounds of Brazilian beans purchased to produce Regular, BD = pounds of Brazilian beans purchased to produce DeCaf, CR = pounds of Colombian beans purchased to produce Regular, and CD = pounds of Colombian beans purchased to produce DeCaf.) Max 2.033BR+2.582BD+1.868CR+2.418CD INCORRECT Pounds of Regular BR+CR≤900 INCORRECT Pounds of DeCaf BD+CD≤400 INCORRECT
Each year, Paynothing Shoes faces demands (whichmust be met on time) for pairs of shoes as shown in Table37. Workers work three consecutive quarters and then receiveone quarter off. For example, a worker may work duringquarters 3 and 4 of one year and quarter 1 of the next year.During a quarter in which a worker works, he or she canproduce up to 50 pairs of shoes. Each worker is paid $500per quarter. At the end of each quarter, a holding cost of $50per pair of shoes is assessed. Formulate an LP that can beused to minimize the cost per year (labor holding) ofmeeting the demands for shoes. To simplify matters, assume3.11 Multiperiod Financial Models 105that at the end of each year, the ending inventory is zero.(Hint: It is allowable to assume that a given worker will getthe same quarter off during each year.) TAB LE 37Quarter 1 Quarter 2 Quarter 3 Quarter 4600 300 800 100
A library must build shelving to shelve 200 4-inch highbooks, 100 8-inch high books, and 80 12-inch high books. 8.3 Maximum-Flow Problems 419Each book is 0.5 inch thick. The library has several ways tostore the books. For example, an 8-inch high shelf may bebuilt to store all books of height less than or equal to 8inches, and a 12-inch high shelf may be built for the 12-inchbooks. Alternatively, a 12-inch high shelf might be built tostore all books. The library believes it costs $2,300 to builda shelf and that a cost of $5 per square inch is incurred forbook storage. (Assume that the area required to store a bookis given by height of storage area times book’s thickness.)Formulate and solve a shortest-path problem that couldbe used to help the library determine how to shelve thebooks at minimum cost. (Hint: Have nodes 0, 4, 8, and 12,with cij being the total cost of shelving all books of height i and j on a single shelf.)
4 Sunco processes oil into aviation fuel and heating oil. Itcosts $40 to purchase each 1,000 barrels of oil, which isthen distilled and yields 500 barrels of aviation fuel and 500barrels of heating oil. Output from the distillation may besold directly or processed in the catalytic cracker. If soldafter distillation without further processing, aviation fuelsells for $60 per 1,000 barrels, and heating oil sells for $40per 1,000 barrels. It takes 1 hour to process 1,000 barrels ofaviation fuel in the catalytic cracker, and these 1,000 barrelscan be sold for $130. It takes 45 minutes to process 1,000barrels of heating oil in the cracker, and these 1,000 barrelscan be sold for $90. Each day, at most 20,000 barrels of oilcan be purchased, and 8 hours of cracker time are available.Formulate an LP to maximize Sunco’s profits.
Mr. Barrera raises goats and pigs. He wants to raise no more than 16 animals including no more than 10 goats. It will cost $25 to raise each goat and $75 to raise each pig. She will make $12 in profit from each goat and $40 in profit from each pig. She has $900 to raise animals. How many of each type of animal should she raise to maximize profit?

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