Optimization Quiz 1

Question 1

Which of the following is/are incorrect regarding optimization?

Accepted Answer

None of these

Answer

Optimization is the selection of the best element based on a particular criterion from a set of available alternatives.

Answer

Optimization problem is the problem of finding the best solution from all feasible solutions.

Answer

Optimization is a mathematical approach.

Question 2

Which of the following optimization problems exist?

Accepted Answer

Both of the A and B

Answer

Continuous and discrete optimization.

Answer

Constrained and unconstrained optimization

Answer

None of the A and B

Question 3

Determine two negative integers such that the product of two numbers is equal to 785 and the sum of two numbers is maximum.

Accepted Answer

$$x=-\sqrt{785},y=-\sqrt{785}$$

Answer

$$x=-\sqrt{785},y=\sqrt{785}$$

Answer

$$x=\sqrt{785},y=\sqrt{785}$$

Answer

$$x=\sqrt{785},y=-\sqrt{785}$$

Question 4

Consider that $$p$$ and $$q$$ are both real numbers. Find the values of $$p$$ and $$q$$ such that $$p+9q$$ and $$\left( p+7 \right)\left( q+3 \right)$$ is maximum?

Accepted Answer

$$p=-7, q=-3$$

Answer

$$p=-7, q=3$$

Answer

$$p=7, q=-3$$

Answer

$$p=7, q=3$$

Question 5

A cricket ground is in a shape as shown in below figure. There is a material whose length is 750 ft which is required for fencing of the cricket ground. Let us assume the total maximum area of the ground is equal to $${{A}_{\max }}$$. Then find the value of $${{A}_{\max }}$$ $$ \ $$ <img  src="https://cmds-vedantu.s3.ap-southeast-1.amazonaws.com/prod/question-sets/19373b93-9e3c-4345-8f90-ff8c3f3b383b781556022914038782.png"/>

Accepted Answer

$${{A}_{\max }}=\dfrac{{{\left( 375+\pi  \right)}^{2}}}{2\pi }$$

Answer

$${{A}_{\max }}=\dfrac{{{\left( 375+2\pi  \right)}^{2}}}{\pi }$$

Answer

$${{A}_{\max }}=\dfrac{{{\left( 375+2\pi  \right)}^{2}}}{2\pi }$$

Answer

$${{A}_{\max }}=\dfrac{{{\left( 375+2\pi  \right)}^{2}}}{\pi }$$