APM261: Quiz 2. Geometric Solutions and Linear Algebra

Quiz 2. Geometric Solutions and Linear Algebra

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Each question has only one correct answer. The results of the quiz do not affect the final marks.

1: Which statement is true?

Objective function in Linear Programming problems has always finite value at the optimal solution
A finite optimal solution can be not unique
Feasible regions are classified into bounded, unbounded, empty and multiple
Corner points of a feasible region are located at the intersections of the region and coordinate axes

2: Identify the type of the feasible region given by the set of inequalities

x - y <= 1
x - y >= 2

where both x and y are positive.

A triangle
A rectangle
An unbounded region
An empty region

3: Consider the given vectors: a(2,0), b(0,2), c(1,1), and d(0,3). Which of the following vectors are linearly independent?

a, b, and c are independent
a, b, and d are independent
a and c are independent
b and d are independent

4: Consider the linear equation

2 x₁ + 3 x₂ - 4 x₃ + 5 x₄ = 10

How many basic and non-basic variables are defined by this equation?

One variable is basic, three variables are non-basic
Two variables are basic, two variables are non-basic
Three variables are basic, one variable is non-basic
All four variables are basic

5: The objective function for a minimization problem is given by

z = 2 x₁ - 5 x₂ + 3 x₃

The hyperplane for the objective function cuts a bounded feasible region in the space (x₁,x₂,x₃). Find the direction vector d, where a finite optimal solution can be reached.

d(2,-5,3)
d(-2,5,-3)
d(2,5,3)
d(-2,-5,-3)

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