Imagine a manufacturing company that produces standardized products using highly controlled and predictable processes. The company has a well-documented history of production data and precise quality control measures.

In which situation would the company likely prefer to use deterministic models for production planning?

• When the problem's information is uncertain

• When there's a range of potential results

• When information about the problem is known with a high degree of certainty

• When probabilities are incorporated into the problem

Consider a weather forecasting agency trying to predict rainfall for the upcoming week in a region prone to varied weather conditions. They have historical data but face unpredictable weather patterns.

In this scenario, when would probabilistic models be most advantageous for predicting rainfall?

• When the problem's information is known with certainty

• When average or expected results are needed

• When there is complete knowledge about a problem

• When the model forces a specific outcome

Which of the following variables is considered random or probabilistic?

• future interest rates

• last year's advertising budget

• last week's sales data

• historical stock prices

Solve the following linear program graphically and determine the number of extreme points that exist for this problem:

Minimize 150X+210Y Subject to:

1. 3.8X+1.2Y≥22.8

2.  Y≥6

3.  Y≤15

4.  45X+30Y=630

5.  X,Y≥0

How many extreme points are present in the feasible region when graphically solving this linear program?

• 2

• 3

• 4

• 5

A company makes two products, A and B. A sells for $100 and B sells for $90. The variable production costs are $30 per unit for A and $25 for B. The company's objective could be written as: Max 190x1 − 55x2.

• True

• False

Are any of the constraints redundant? If yes, identify the constraint that is redundant.

 

• Constraint 1: X+Y≤3

• Constraint 2: X−2Y≥0

• Constraint 3: Y≤1

• There are no redundant constraints

Use this graph to answer the questions

Which area forms the feasible region?

• Area I

• Area II

• Area III

• AVrea IV

Use this graph to answer the questions

Which constraints are binding?

• Constraints 1 and 2

• Constraints 2 and 3

• Constraint 1

• Constraint 2

Use this graph to answer the questions. Which point is optimal?

• E

• A

• B

• D

Which of the following is the correct statement about duality in linear programming?

• The dual problem is always a minimization problem.

• The dual problem has the same optimal solution as the primal problem.

• The dual problem is always feasible if the primal problem is infeasible.

• The dual problem always has a feasible solution.