Maximizing Returns and Decision Variables

Maximizing Returns and Decision Variables

Assessment

Interactive Video

Mathematics

11th - 12th Grade

Practice Problem

Hard

Created by

Thomas White

FREE Resource

This tutorial introduces linear integer programming models using binary or 0-1 variables, focusing on decision-making in yes or no situations. It covers project selection models, where binary variables indicate project selection, and fixed cost problems, where binary variables determine machine usage. The tutorial demonstrates how to maximize returns and minimize costs using these models, with examples of constraints and objective functions. The video concludes with a preview of the next tutorial on relational constraints using binary variables.

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19 questions

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1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the primary use of binary variables in decision-making?

To determine project duration

To calculate project costs

To indicate a yes or no decision

To represent continuous variables

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How is the decision variable defined for project selection?

X1 = 0 if project 1 is selected

X1 = 1 if project 1 is not selected

X1 = 0 if project 1 is selected

X1 = 1 if project 1 is selected

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the objective when formulating the function for project selection?

Minimize costs

Minimize project risks

Maximize returns

Equalize project durations

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which of the following represents the objective function for maximizing returns?

X1 ≤ 400, X2 ≤ 550, X3 ≤ 600

58X1 + 44X2 + 26X3 + 23X4

217X1 + 125X2 + 88X3 + 109X4

X1 + X2 + X3 + X4

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What constraint is applied to project outlays?

They must equal available funds

They are not constrained by available funds

They must be greater than available funds

They must be less than or equal to available funds

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which software can be used to solve the linear integer programming model?

MATLAB

Python

LINDO or Excel Solver

R

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the optimal solution for project selection to maximize returns?

X1 = 0, X2 = 1, X3 = 0, X4 = 1

X1 = 1, X2 = 0, X3 = 1, X4 = 1

X1 = 1, X2 = 1, X3 = 0, X4 = 0

X1 = 0, X2 = 0, X3 = 1, X4 = 1

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