Optimization Problems

Q.

Where is linear algebra used in real life?

Q.

A Furniture dealer deals in only two items, table and chair. He has $Rs.5000$ to invest and a space to store at most $60$ pieces. A table costs him $Rs.250$ and a chair $Rs.50$. He can sell a table at a profit of $Rs.50$ and a chair at a profit of $Rs.15$. Assume that, he can sell all the items that he produced. The number of constraints in the problem is

1. $2$

2. $3$

3. $4$

4. $5$

Q.

All linear programming problems have all of the following properties EXCEPT

1. A set of linear constraints

2. Variables that are all restricted to nonnegative values

3. A linear objective function that is to be maximized or minimized

4. Alternative optimal solutions

Q. Minimise and Maximise Z = x + 2 y subject to .

Q.

Problems which seek to maximise or, minimise profit or, cost form a general class of problems called ………

1. Non-linear problems

2. Simple problems

3. Optimisation problems

4. Difficult problems

Q. Bat and Ball are partners sharing the profits in the ratio of $2:3$ with capitals of $Rs.1,20,000$ and $Rs.60,000$ respectively. On 1st October, 2017, Bat and Ball granted loans of $Rs.2,40,000$ and $Rs.1,20,000$ respectively to the firm. Bat had allowed the firm to use his property for business for a monthly rent of $Rs.5,000$. The loss for the year ended 31st March, 2018 before rent and interest amounted to $Rs.9,000$. Show distribution of profit/loss.

Q. A manufacturing company makes two types of teaching aids A and B of Mathematics for class XII. Each type of A requires 9 labour hours of fabricating and 1 labour hour for finishing. Each type of B requires 12 labour hours for fabricating and 3 labour hour for finishing. For fabricating and finishing, the maximum labour hours available per week are 180 and 30 respectively. The company makes a profit of Rs. 80 on each piece of type A and Rs. 120 on each piece of type B. How many pieces of type A and type B should be manufactured per week to get a maximum profit? Make it as an LPP and solve graphically. What is the maximum profit per week?

Q. Maximise Z = 3 x + 4 y Subject to the constraints:

Q. Maximise Z = x + y , subject to .

Q. Which of the following is not an optimisation problem?

1. Maximising profit

2. Minimising Area

3. Minimizing cost

4. Finding Area

Q.

How does linear programming help in decision making?

Q.

A linear function of several variables x and y is called ……...

1. Objective function

2. Non-linear function

3. Optimal function

4. Simple function

Q.

What is significance of linear programming in research methodology?

Q. Which of the following is not an optimisation problem?

1. Maximising profit

2. Minimizing cost

3. Finding Area

4. Minimising Area

Q. Linear programming used to optimize mathematical procedure and is

1. subset of mathematical programming
2. dimension of mathematical programming
3. linear mathematical programming
4. all of above

Q. A merchant plans to sell two products $A$ and $B$ costs $\text{Rs}25000$ and $\text{Rs}40000$ respectively. He estimates that the total monthly demand of products will not exceed $250$ units. If he does not want to invest more than $\text{Rs}70$ lakhs and if his profits on product $A$ is $\text{Rs}4500$ and on $B$ is $\text{Rs}5000.$ Then number of products $A$ stocked to get maximum profit is

Q. From the following options given below, the problem that is not an optimisation problem is .

1. maximising profit
2. minimizing cost
3. finding area of a square
4. minimising Area

Q. Minimize: $Z=6x+4y$
Subject to : $3x+2y\ge 12$,
$x+y\ge 5$,
$0\le x\le 5$,
$0\le y\le 6$

Q. Maximise Z = 3 x + 2 y subject to .

Q. The corner points of the feasible region determined by the following system of linear inequalities: Let Z = px + qy , where p , q > 0. Condition on p and q so that the maximum of Z occurs at both (3, 4) and (0, 5) is (A) p = q (B) p = 2 q (C) p = 3 q (D) q = 3 p

Q. In an optimisation problem we are only concerned about maximizing profits.

1. True
2. False

Q.

A manufacturer make two types of toys A and B. Three machines are needed for this purpose and the time (in minutes) required for each toy on the machines is given below.
$\begin{array}{cccc}Types& & Machines& \\ & I& II& III\\ A& 12& 18& 6\\ B& 6& 0& 9\end{array}$
Each machine is available for a maximum of 6 h per day. If the profit on each toy of type A is Rs.7.50 and that the each toy of type B is Rs. 5, show that 15 toys of type A and 30 of type B should be manufactured in a day to get maximum profit.

Q. Which of the terms is not used in a linear programming problem?

1. Feasible solution
2. Concave region
3. Optimal solution
4. Objective function

Q. Maximise Z = − x + 2 y , subject to the constraints: .

Q. Minimise Z = −3 x + 4 y subject to .

Q. Minimise Z = 3 x + 5 y such that .

Q. Minimise Z = x + 2 y subject to .

Q.

Solve the inequality. Graph the solution.

$4k–8\ge 20$

Q. Minimise and Maximise Z = 5 x + 10 y subject to .

Q. The lines $x+y=|a|$ and $ax-y=1$ intersect each other in the first quadrant. Then the set of all possible values of $a$ in the interval are

1. $[1,\infty )$
2. $(1,\infty )$
3. $(-1,\infty )$
4. $(-1,1]$