This is a separable differential equation hence we may write

This may be rewritten as

if we say

then the solution is

The correct answer is A.

Since A is type of 2x3 and B is type of 3x1 then the matrix A^.B must be type of 2x1. When we multiply these matrices we obtain

maximum {-1,0,-8}=0 and minimum {2,4,6,3}=2. Hence, 2+0=2. So the answer is D.

It is known that in a complete graph all of the vertices are adjacent to each other.

If the first player chooses 2nd row, the guaranteed value (income) for him is the minimal element of this row. minimum {1,3,4,2} = 1. Hence the answer is B.

The total revenue function may be found by integrating the marginal revenue, so that we have

Now we need to calculate R(30) – R(20) .

Hence the answer is D.

Since 

then

is obtained.  Since

is given, we  should have

From this equation one has

Then answer is  

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

maximum {-3,-4,-1} = -1, minimum {2,-1,6,7} = -1. There exists an equilibrium pair (3rd row, 2nd column). The number -1, which lies in the intersection of 3rd row and 2nd column, is the lowest in the 3rd  row, is the greatest in the 2nd column. Answer is D.

Since only b,c,d,e are adjacent to a, the answer is A.

We know by Euler’s theorem on planar graphs that the number of edges is equal to m = f + (n -2). Hence, the number of edges is 5+ (4 – 2) = 7. Answer is C.

We can directly calculate the integral

The correct answer is E.

minimum {4,0,2,2,3}=0. The number 0 corresponds to the 2nd column. Hence the answer is B.

The lower value is the guaranteed result for Player I, the upper value is the guaranteed result for Player II. Player I, by choosing a row, maximizes the obtained element. Considering this, player needs to analyze each row to find the lower value on each row and then choosing the maximum among those numbers will give him the result. Each row has the lower value -6, -3 and -4 respectively. So max {-3, -4, -6} =-3 is obtained hence the correct answer is B.

The constraint set has five corner points:

The maximum value of the goal function at these points is attained at the point

This value is 23.
The correct answer is D.

The total revenue function may be found by integrating the marginal revenue, so that we have

Now we need to calculate R(20) – R(10) and since we are taking a difference we do not need the value of the integration constant c.

Therefore the correct answer is the E option.

If in the game matrix, there exists an element which is smallest in its row and greatest in its column then this row-column pair is an equilibrium pair. For each row write the lowest element to the right, and for each column write the greatest element below the matrix:

Now, observe that max {-1, 0, 2} = 2 and min {2, 3, 4} = 2. Therefore, (2nd row, 3rd column) is an equilibrium pair. The correct answer is D.

is straight line with  x-axis intercept (3,0), y-axis intercept (0,2). The point (0,0)  statisfies

therefore  (0,0)  belongs to the half plane

Correct answer is B

Let us put

and substitute it into the differential equation. Then the characteristic equation is

We can write the solution like

Using initial conditions

we have

Hence

The correct answer is D.