运筹学作业

Property
Alloy
1 2 3 4 5
Percentage of tin
Percentage of zinc
Percentage of lead
60 25 45 20 50
10 15 45 50 40
30 60 10 30 10
Cost($/lb)
22 20 25 24 27
The objective is to determine the proportions of these alloys that should be blended to produce the new alloy at a minimum cost.
Nutritional
Ingredient
Kilogram
Of
Corn
Kilogram
falfa
Minimum
Daily
Requirement
Carbohydrates
90
20
40
200
Protein
30
80
60
180
Vitamins
10
20
60
150
Cost
（2）Problem2
You are given the following data for a linear programming problem where the objective is to maximize the profit from allocating three resources to two nonnegative activities.
OR Experiment Report
Experiment No. :1
Student name: Zhang Huiyi Class:Industrial Engeering 2010th.NO.2
Student Number:20102659
Tutor: Tao Fengming Date:2013/1/12
When (x1,x2)=(9,11),the result is
So (x1,x2)=(9,11) is the unfeasible solution.
When (x1,x2)=(11,9),the result is
So (x1,x2)=(11,9) is the unfeasible solution.
(a)Formulate a linear programming model for this problem.
(b)Use the Excel Solver to solve this model by the simplex method.
Experiment Objectives :
Formulate and solve complex linear programming problem using Excel Solver.
Experiment Content:
Problem 1:
The Metalco Company desires to blend a new alloy of 40 percent tin, 35 percent zinc, and 25 percent lead from several available alloys having the following properties:
(a)Formulate a linear programming model for this model.
(b)Use the Graphical method to solve this model.
(c)Display the model on an Excel spreadsheet.
(d)Use the spreadsheet to check the following solutions: (x1,x2)=(5,5), (8,10), (10,8), (8,8), (9,11), (11,9). Which of these solutions are feasible? Which of feasible solutions has the best value of the objective function?
(4) Learn to quickly apply the Excel Solver to find an optimal solution for the model.
Experiment Content:
（1）Problem 1The Wyndor Problem (Reference: Textbook P25 and P67, experimentⅠ)
When (x1,x2)=(10,8),the result is
So (x1,x2)=(10,8) is the feasible solution.
When (x1,x2)=(8,8),the result is
So (x1,x2)=(8,8) is the feasible solution.
Experiment Tool:
The Microsoft Excel (the Solver has been installed).
Experiment Result:
Problem1
a)
b)
c)
Problem2
a)Formulate a linear programming model for this problem.
(e)Use the Excel Solver to solve the model by the simplex method.
Experiment Tool:
The Microsoft Excel (the Solver has been installed).
Experiment Result:
Resource
Resource Usage per
Unit of Each Activity
Amount of Resource
Available
Activity1 Activity2
1
2
3
2 1
3 3
2 4
30
60
60
Contribution
Per unit
$20 $30
Contribution per unit = profit per unit of the activity.
Make x1,x2,x3 represent the amount ofcorn, tankage, and alfalfa.
Minimize z=84x1+72x2+60x3
Subject to 90x1+20x2+40x3>=200
30x1+80x2+60x3>=180
10x1+20x2+60x3>=150
Problem1
a）the linear programming model
Maximize Z=3x1+5x2
Subject tox1<=4
2x2<=12
3x1+2x2<=18
And x1>=0,x2>=0
b)
Problem2
c)
d)the optimal solution of the problem is
From OR Tutor/General Linear ProgrammingRecallthe following contents:
(1)The interpretation of the Slack Variables
(2)The Simplex Method-Algebraic Form
(3)The Simplex Method-Tabular Form
And x1,x2>=0
b)
c)
OR Experiment Report
Experiment No. :3
Student Name: Zhanghuiyi Class:Industrial Engeering 2010th.NO.2
Student Number:20102659
Tutor: Tao Fengming Date:2013/1/12
When (x1,x2)=(5,5),the result is
So (x1,x2)=(5,5) is the feasible solution.
When (x1,x2)=(8,10),the result is
So (x1,x2)=(8,10) is the feasible solution.
Experiment Content:
Problem 1: Consider the following problem:
Maximize Z=2x1+x2
Subject to
x1 +x2 ≤ 40
4x1 +x2 ≤100
and
x1≥0，x2≥0
(1)Work through the simplex method step by step in tabular form.
(x1,x2)=(5,5), (8,10), (10,8), (8,8) are feasible.
(x1,x2)=(10,10) has the best value of the objective function.
e)Use the Excel Solver to solve the model by the simplex method.
Experiment Objectives :