The Texas Consolidated Electronics Company is contemplating a research and development program encompassing eight research projects. The company is constrained from embarking on all projects by the number of available management scientists (40) and the budget available for R&D projects ($300,000). Further, if project 2 is selected, project 5 must also be selected (but not vice versa). Table below lists the resource requirements and the estimated profit for each project. The company wants to decide which of those projects need to be taken on to maximize the total profit for the company. Formulate an integer programming model for this problem. Define x₁, where i=1, 2, 3, ... 8 such that if x=1, project i would be taken on; and if x=0, project i would not. Define Z as the total profit ($1,000,000). Which of the following objective function is correct? Expense ($1,000s) Management Scientists Required Estimated Profit ($1,000,000s) Project 1 $ 60 7 $0.36 2 110 9 0.82 3 53 8 0.29 4 47 4 0.16 5 92 7 0.56 6 85- 6 0.61 73 8 0.48 8 65 5 0.41 Maximize Z-.36x1+.82x2+.29x3+.16x4+.56x5+.61x6+.48x7+.41x8 O Maximize Z-x1+x2+x3+x4+x5+x6+x7+x8 O Maximize Z-60x1+110x2+53x3+47x4+92x5+85x6+73x7+65x8 O Maximize Z-(.36+.82+.29+.16+.56+.61+.48+.41)(x1+x2+x3+x4+x5+x6+x7+x8)
The Texas Consolidated Electronics Company is contemplating a research and development program encompassing eight research projects. The company is constrained from embarking on all projects by the number of available management scientists (40) and the budget available for R&D projects ($300,000). Further, if project 2 is selected, project 5 must also be selected (but not vice versa). Table below lists the resource requirements and the estimated profit for each project. The company wants to decide which of those projects need to be taken on to maximize the total profit for the company. Formulate an integer programming model for this problem. Define x₁, where i=1, 2, 3, ... 8 such that if x=1, project i would be taken on; and if x=0, project i would not. Define Z as the total profit ($1,000,000). Which of the following objective function is correct? Expense ($1,000s) Management Scientists Required Estimated Profit ($1,000,000s) Project 1 $ 60 7 $0.36 2 110 9 0.82 3 53 8 0.29 4 47 4 0.16 5 92 7 0.56 6 85- 6 0.61 73 8 0.48 8 65 5 0.41 Maximize Z-.36x1+.82x2+.29x3+.16x4+.56x5+.61x6+.48x7+.41x8 O Maximize Z-x1+x2+x3+x4+x5+x6+x7+x8 O Maximize Z-60x1+110x2+53x3+47x4+92x5+85x6+73x7+65x8 O Maximize Z-(.36+.82+.29+.16+.56+.61+.48+.41)(x1+x2+x3+x4+x5+x6+x7+x8)
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter11: Simulation Models
Section: Chapter Questions
Problem 69P: The Tinkan Company produces one-pound cans for the Canadian salmon industry. Each year the salmon...
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Transcribed Image Text:In the model formulation of the Texas Consolidated Electronics Company problem, the constraint
regarding project 2 and project 5 is
Ⓒx2+x5>=1
O x2+x5<=1
O x2-x5>=0
O x2-x5<=0
Transcribed Image Text:The Texas Consolidated Electronics Company is contemplating a research and development program
encompassing eight research projects. The company is constrained from embarking on all projects by
the number of available management scientists (40) and the budget available for R&D projects
($300,000). Further, if project 2 is selected, project 5 must also be selected (but not vice versa). Table
below lists the resource requirements and the estimated profit for each project. The company wants
to decide which of those projects need to be taken on to maximize the total profit for the company.
Formulate an integer programming model for this problem. Define x₁, where i=1, 2, 3, ... 8 such that
if x=1, project i would be taken on; and if x=0, project i would not. Define Z as the total profit
($1,000,000). Which of the following objective function is correct?
Expense
($1,000s)
Management
Scientists Required
Project
Estimated Profit
($1,000,000s)
I
$ 60
7
$0.36
2
110
9
0.82
53
8
0.29
4
47
4
0.16
5
92
7
0.56
6
85-
6
0.61
7
73
8
0.48
8
65
5
0.41
Maximize Z=.36x1+.82x2+.29x3+.16x4+.56x5+.61x6+.48x7+.41x8
O Maximize Z-x1+x2+x3+x4+x5+x6+x7+x8
O Maximize Z=60x1+110x2+53x3+47x4+92x5+85x6+73x7+65x8
O Maximize Z=(.36+.82+.29+.16+.56+.61+.48+.41)(x1+x2+x3+x4+x5+x6+x7+x8)
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