## Quiz 1. Introduction to Operation Research

Each question has only one correct answer. The results do not affect your final marks.

1: What is the objective function in linear programming problems?

A constraint for available resource
An objective for research and development of a company
A linear function in an optimization problem
A set of non-negativity conditions

2: Which statement characterizes standard form of a linear programming problem?

Constraints are given by inequilities of any type
Constraints are given by a set of linear equations
Constraints are given only by inequalities of >= type
Constraints are given only by inequalities of <= type

3: Maximize `z = 2 x + 7 y` subject to

3 x - 2 y <= 1
- x + 3 y >= -1

for non-negative `x` and `y`. Which of the following points are feasible: `A(0,0), B(1,1), C(2,2)`?

`A`, `B`, and `C`
`A` and `B`
`A` and `C`
`B` and `C`

4: Consider the constraint

5 x + 3 y - 4 z <= 7

Find the value of the slack variable `s` associated to this constraint for the point `A(1,2,3)`.

`s = 8`
`s = 6`
`s = 0`
`s = -1`

5: Maximize ` z = 3x ` for ` 0 <= x <= 5 `. Find an optimal solution of the problem.

` x = 0`
` x = 1`
` x = 3`
` x = 5`