Question 1

Which one of the following represents one of the constraints in question 9?

Accepted Answer

A) $3 s-3 c+a \geq 0$ 
B) $a+c+s \leq 7$ 
C) $3 c+3 s+a \leq 0$ 
D) $17 s+10 a+13 c \leq 250$ 
E) $c \leq 2 s$ 
A) $3 s-3 c+a \geq 0$ 
B) $a+c+s \leq 7$ 
C) $3 c+3 s+a \leq 0$ 
D) $17 s+10 a+13 c \leq 250$ 
E) $c \leq 2 s$ D

Question 2

What can you say about the solution of the linear programming problem specified in question 5, if the second constraint is changed to$x+y \leq 2$ and the problem is one of minimization?

Accepted Answer

A) Unique solution at (0, 12) 
B) Unique solution at (0, 2) 
C) Unique solution at (2, 0) 
D) Infinitely many solutions 
E) No solution 
A) Unique solution at (0, 12) 
B) Unique solution at (0, 2) 
C) Unique solution at (2, 0) 
D) Infinitely many solutions 
E) No solution B

Question 3

What can you say about the linear programming problem specified in question 5, if the second constraint is changed to $3 x-4 y \leq 24$ and the problem is one of maximization?

Accepted Answer

A) No solution 
B) Infinitely many solutions 
C) Unique solution at (8, 0) 
D) Unique solution at (0, 6) 
E) Unique solution at (0, 0) 
A) No solution 
B) Infinitely many solutions 
C) Unique solution at (8, 0) 
D) Unique solution at (0, 6) 
E) Unique solution at (0, 0) B

Question 4

The point (x, 3)satisfies the inequality, $-5 x-2 y \leq 13$. Find the smallest possible value of x.

Accepted Answer

A) - 3.8 
B) - 1.4 
C) 0 
D) 3.8 
E) 1.4 
A) - 3.8 
B) - 1.4 
C) 0 
D) 3.8 
E) 1.4

Question 5

Leo has $12.50 to spend on his weekly supply of sweets, crisps and apples. A bag of crisps costs $0.65, a bag of sweets costs $0.85, and one apple costs $0.50. The total number of packets of crisps, sweets and apples consumed in a week must be at least seven, and he eats at least twice as many packets of sweets as crisps. His new healthy diet also means that the total number of packets of sweets and crisps must not exceed one- third of the number of apples. If s, c and a, denote the number of packets of sweets, packets of crisps, and apples respectively, which one of the following represents one of the constraints defining the feasible region?

Accepted Answer

A) $3 c+3 s \leq a$ 
B) $0.65 s+0.85 c+0.5 a \geq 12.5$ 
C) $s \geq 0.5 c$ 
D) $a+c+s>7$ 
E) $s \leq c-a$ 
A) $3 c+3 s \leq a$ 
B) $0.65 s+0.85 c+0.5 a \geq 12.5$ 
C) $s \geq 0.5 c$ 
D) $a+c+s>7$ 
E) $s \leq c-a$

Question 6

How many points with integer coordinates lie in the feasible region defined by $3 x+4 y \leq 12, x \geq 0 \text { and } y \geq 1 ?$

Accepted Answer

A) 8 
B) 5 
C) 7 
D) 4 
E) 6 
A) 8 
B) 5 
C) 7 
D) 4 
E) 6

Question 7

Find, if possible, the minimum value of the objective function 3x - 4y subject to the constraints $-2 x+y \leq 12, x-y \leq 2, x \geq 0 \text { and } y \geq 0$

Accepted Answer

A) - 36 
B) 0 
C) - 8 
D) No solution 
E) 8 
A) - 36 
B) 0 
C) - 8 
D) No solution 
E) 8

Question 8

How many of the following points satisfy the inequality 2x - 3y > - 5? 
(1, 1), (- 1, 1), (1, - 1), (- 1, - 1), (- 2, 1), (2, - 1), (- 1, 2)and (- 2, - 1)

Accepted Answer

A) 3 
B) 4 
C) 5 
D) 6 
E) 7 
A) 3 
B) 4 
C) 5 
D) 6 
E) 7

Question 9

What can you say about the solution of the linear programming problem specified in question 5, if the objective function is to be maximised instead of minimized?

Accepted Answer

A) Unique solution at (0, 12) 
B) Infinitely many solutions 
C) Unique solution at (0, 0) 
D) No solution 
E) Unique solution at (2, 0) 
A) Unique solution at (0, 12) 
B) Infinitely many solutions 
C) Unique solution at (0, 0) 
D) No solution 
E) Unique solution at (2, 0)

Question 10

The following five inequalities define a feasible region. Which one of these could be removed from the list without changing the region?

Accepted Answer

A) $x-2 y \geq-8$ 
B) $x \geq 0$ 
C) $y \geq 0$ 
D) $-x+y \leq 10$ 
E) $x+y \leq 20$ 
A) $x-2 y \geq-8$ 
B) $x \geq 0$ 
C) $y \geq 0$ 
D) $-x+y \leq 10$ 
E) $x+y \leq 20$

Which one of the following represents one of the constraints in question 9?

What can you say about the solution of the linear programming problem specified in question 5, if the second constraint is changed to $x+y \leq 2$ and the problem is one of minimization?

What can you say about the linear programming problem specified in question 5, if the second constraint is changed to $3 x-4 y \leq 24$ and the problem is one of maximization?

The point (x, 3)satisfies the inequality, $-5 x-2 y \leq 13$ . Find the smallest possible value of x.

How many points with integer coordinates lie in the feasible region defined by $3 x+4 y \leq 12, x \geq 0 \text { and } y \geq 1 ?$

Find, if possible, the minimum value of the objective function 3x - 4y subject to the constraints $-2 x+y \leq 12, x-y \leq 2, x \geq 0 \text { and } y \geq 0$

How many of the following points satisfy the inequality 2x - 3y > - 5? (1, 1), (- 1, 1), (1, - 1), (- 1, - 1), (- 2, 1), (2, - 1), (- 1, 2)and (- 2, - 1)

What can you say about the solution of the linear programming problem specified in question 5, if the objective function is to be maximised instead of minimized?

The following five inequalities define a feasible region. Which one of these could be removed from the list without changing the region?

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Exam 8: Linear Prgamming

Which one of the following represents one of the constraints in question 9?

What can you say about the solution of the linear programming problem specified in question 5, if the second constraint is changed to x+y≤2x+y \leq 2x+y≤2 and the problem is one of minimization?

What can you say about the linear programming problem specified in question 5, if the second constraint is changed to 3x−4y≤243 x-4 y \leq 243x−4y≤24 and the problem is one of maximization?

The point (x, 3)satisfies the inequality, −5x−2y≤13-5 x-2 y \leq 13−5x−2y≤13 . Find the smallest possible value of x.

How many points with integer coordinates lie in the feasible region defined by 3x+4y≤12,x≥0 and y≥1?3 x+4 y \leq 12, x \geq 0 \text { and } y \geq 1 ?3x+4y≤12,x≥0 and y≥1?

Find, if possible, the minimum value of the objective function 3x - 4y subject to the constraints −2x+y≤12,x−y≤2,x≥0 and y≥0-2 x+y \leq 12, x-y \leq 2, x \geq 0 \text { and } y \geq 0−2x+y≤12,x−y≤2,x≥0 and y≥0

How many of the following points satisfy the inequality 2x - 3y > - 5? (1, 1), (- 1, 1), (1, - 1), (- 1, - 1), (- 2, 1), (2, - 1), (- 1, 2)and (- 2, - 1)

What can you say about the solution of the linear programming problem specified in question 5, if the objective function is to be maximised instead of minimized?

The following five inequalities define a feasible region. Which one of these could be removed from the list without changing the region?

Linear Equations

Non-Linear Equations

Mathematics of Finance

Differentiation

Partial Differentiation

Integration

Matrices

Dynamics

Filters

What can you say about the solution of the linear programming problem specified in question 5, if the second constraint is changed to $x+y \leq 2$ and the problem is one of minimization?

What can you say about the linear programming problem specified in question 5, if the second constraint is changed to $3 x-4 y \leq 24$ and the problem is one of maximization?

The point (x, 3)satisfies the inequality, $-5 x-2 y \leq 13$ . Find the smallest possible value of x.

How many points with integer coordinates lie in the feasible region defined by $3 x+4 y \leq 12, x \geq 0 \text { and } y \geq 1 ?$

Find, if possible, the minimum value of the objective function 3x - 4y subject to the constraints $-2 x+y \leq 12, x-y \leq 2, x \geq 0 \text { and } y \geq 0$