Linear Programming Problems

Q.

What are the limitations of linear programming problem?

Q. The equations of the circles touching both the axes and passing through the point (1, 2) are

1. 
2. 
3. 
4. None of these

Q.

Infeasibility means that the number of solutions to the linear programming models that satisfies all constraints is

1. At least 1

2. Zero

3. At least 2

4. An infinite number

Q.

A feasible solution of a LPP if it also optimizes the objective function is called

1. None of these

2. Optimal feasible solution

3. Optimal solution

4. Feasible solution

Q. The shaded region in the figure is the solution set of the inequations

1. $6x+4y\ge 24,x\le 4,y\le 5,x,y\ge 0$
2. $6x+4y\le 24,x\ge 4,y\le 5,x,y\ge 0$
3. $6x+4y\le 24,x\ge 4,y\ge 5,x,y\ge 0$
4. $6x+4y\ge 24,x\ge 4,y\le 5,x,y\ge 0$

Q.

What are the applications of linear programming?

Q.

Explain why the graphing calculator cannot be used to solve or approximate solutions to all polynomial equations.

Q.

What companies use linear programming?

Q.

A ……… of a feasible region is a point in the region, which is the intersection of two boundary lines.

1. Section point

2. Vertex point

3. Reasonable point

4. Corner point

Q.

Maximum Z=3x +4y, subject to the constraints $x+y\le 1,x\le 0,y\le 0$.

Q.

Find the vector and the Cartesian equations of the line that passes through the origin and (5, - 2, 3).

Q. Let total revenue received from the sale of $x$ units of a product is given by $R\left(x\right)=12x+2x^2+6.$
Then the actual revenue from selling the ${51}^{\text{st}}$ item is

[2 marks]

1. $214$
2. $202$
3. $212$
4. $200$

Q.

What is a graphical method in linear programming?

Q. The shaded region in the figure is the solution set of the inequations

1. $6x+4y\ge 24,x\le 4,y\le 5,x,y\ge 0$
2. $6x+4y\le 24,x\ge 4,y\le 5,x,y\ge 0$
3. $6x+4y\ge 24,x\ge 4,y\le 5,x,y\ge 0$
4. $6x+4y\le 24,x\ge 4,y\ge 5,x,y\ge 0$

Q.

Fidel has a rare coin worth $\$550$.

Each decade, the coins value increases by $10\%$.

Which expression gives the coins value, $6$ decades from now?

1. ${\left(550·0.1\right)}^6$

2. $550{\left(1+0.1\right)}^6$

3. $550+{\left(0.1\right)}^6$

4. $550+{\left(1+0.1\right)}^6+{\left(1+0,1\right)}^6$

Q. If the constraints in linear programming problem are changed

1. the problem is to be re-evaluated
2. solution is not defined
3. the change in constraints is ignored
4. the objective function has to be modified

Q. If $6P\left(A\right)=8P\left(B\right)=14P(A\cap B)=1$, then $P\left(A^{\prime }|B\right)=$_______

1. $\frac{3}{7}$
2. $\frac{4}{7}$
3. $\frac{3}{5}$
4. $\frac{2}{5}$

Q.

You are selling T-shirts to raise money for a charity. You sell the T-shirts for $\$10$ each.

Part A
You have already sold 2 T-shirts. How many more T-shirts must you sell to raise at least $\$500$? Explain.
Part B
Your friend is raising money for the same charity and has not sold any T-shirts previously. He sells the T-shirts for $\$8$ each. What are the total numbers of T-shirts he can sell to raise at least $\$500$? Explain.
Part C
Who has to sell more T-shirts in total? How many more? Explain.

Q. Linear programming model which involves funds allocation of limited investment is classified as

1. ordination budgeting model
2. funds investment models
3. capital budgeting models
4. funds origin models

Q.

Show that the solution set of the following linear inequations is empty set:

(i) $x-2y\ge 0,2x-y\le -2,x\ge 0,y\ge 0$

(ii) $x+2y\le 3,3x+4y\ge 12,y\ge 1,x\ge 0andy\ge 0$

Q.

Aman bought a bike for $Rs50000$ and paid $Rs1000$ as transportation charges. He sold for $Rs55000$. Find profit or loss

Q.

Draw the graph of the following equations. Also Determine the Coordinates of the vertices of the triangle formed by these lines and the x-axis.

$4x-5y+16=0;2x+y-6=0$

Q.

Find the linear inequations for which the solution set is the shaded region given in figure.

Q.

A man rides his motorcyle at the speed of 50 km/h. He has to spend Rs 2 per km on petrol. If he rides it at a faster speed of 80 km/h, the petorl cost increases to Rs 3 per km. He has atmost Rs 120 to spend on petrol and one hour's time. He wishes to find the maximum distance that he can travel. Express this problem as a linear programming problem.

Q. Which of the following is a property of all linear programming problems?

1. alternate courses of action to choose from
2. minimization of some objective
3. usage of graphs in the solution
4. usage of linear and nonlinear equations and inequalities
5. a computer program

Q.

Represent to solution set of each of the following in equations graphically in two dimensional plane :
$x\le 8-4y$

Q.

Show that the solution set of the following linear in equations is an unbounded set :

$x+y\ge 9,3x+y\ge 12,x\ge 0,y\ge 0$

Q. The feasible solution of an LP problem, is ________

1. must satisfies all of the problem's constraints simultaneously
2. must be a corner point of the feasible region
3. need not satisfy all of the constraints, only some of them
4. must optimize the value of the objective function

Q. Find the vector and cartesian equations of the line passing through the point (1, 2, -4) and perpendicular to the two lines
$\frac{x-8}{3}=\frac{y+19}{-16}=\frac{z-10}{7}$ and $\frac{x-15}{3}=\frac{y-29}{8}=\frac{z-5}{-5}$

Q.

Represent to solution set of each of the following in equations graphically in two dimensional plane :

$3x-2y\le x+y-8$