Therefore the correct answer is the E option.

We can calculate the Gini index by using the formula 

Lorenz curve. Inserting the given in the question, we find 

The coefficient matrix of the linear system is

and the determinant of

is 6.

The matrix A is a

matrix and the matrix B is a

matrix which means multiplying them will give a

matrix. Now observe that

Therefore the correct answer is E.

The corner  points are (0,0) , (0,8) , (7,0) , (6,2)  Evaluate the values of the goal function      

The maximizing point is (6,2) and the maximum value is 54.

Correct answer is D

Since given matrix has 3 rows and 4 columns it is the type of 3x4.

For the  point (11,4)

Correct answer is C

Firstly, we need to determine the total cost function. This is achieved by integration as

For each row write the lowest element to the right and for each column write the greatest element  below the matrix

There exists an equilibrium  pair  ( 2 nd row 2 nd  column) the number 1 , which lies in the intersection of 2 st row, 2 st column is the lowest in the 2 st row, is the greatest in the 2 st column. Correct answer is  E .

The region is intersection of the solution sets of the inequalities

Therefore the constraints of the problem are  

Let us use the integration by parts method. Let

which gives

Also, let

which gives

Substituting these values into

we get;

Therefore, the correct answer is C.

Player I, by choosing a row, maximizes the obtained element. The lowest elements of the rows are -2, -1 and 0 respectively. The greatest among those values is 0 on the 3^rd row which will be the maximin strategy for Player I. The correct answer is C.

If the system has infinitely many solutions (which means that the equations must coincide), then we know that one of the equations is a scalar multiple of the other one. We see that the coefficients of the second equation is 3/2 multiple of the first one. So it is clear that 

The determinant

is evaluated from the Sarrus’ rule as  

Correct answer is  B

We need to calculate the integral of the production rate over the interval 2 ? t ? 5 which gives

Hence the solution is B.