Let us consider the trial solution 

we can substitute these functions into the equation:

So the general solution is 

The total revenue function can be found by integrating the marginal revenue function, thus we have

Now, we should calculate R(20)-R(10).

If we integrate the marginal revenue, we obtain the total revenue. So,

Since the fixed cost 180TL, we find that c=180. If we denote the quantity to be sold to gain 36TL by q₀ then we arrive at the equality:

By using the property of definite integral, we  can write

then we get

Then the correct answer is B.

Therefore the correct answer is the E option.

Using the points 0, , 1, let us divide the interval into two subintervals ,

has a maximum value M_i on the each subinterval. That is

the correct answer is A.

We first calculate the quantity when the price is 9TL. Using the supply function, we find

which gives q = 2. Inserting the given values in the formula

we obtain

Hence the correct answer is D.

Let u=8x²+2 which means  du=16xdx. If we write the integral with respect to the new variable u we have

For , let A₁ denote the area of the triangle under the x-axis and above the graph. For  let A₂ denote the area of the triangle.

If we make a change of variables as

we get,

Returning back to the original variable x, we find that the antiderivative of f is

. Thus, the definite integral is

Therefore the correct answer is the D option.

Therefore the correct answer is the C option.

The consumer surplus is evaluated taking into account the demand function.

 Since the equilibrium point is

 and

we have

Then the answer is C.

Let us calculate the Gini index for the first function. Inserting the Lorenz function into the formula for the Gini index given above, we obtain

This integral can be calculated by change of variables. Let

then we get

Returning back to the original variable x, we find that the antiderivative of

Thus the definite integral is

The correct answer is D.

To solve this problem, we should use

If we say

We know that

Cancelling the factor

and taking the logarithms of both sides

is found as

Hence, we have,

Lastly, to find

we will use

Thus, 

The correct answer is A.

the correct answer is A.

According to the statement of the problem we wish to have a mass of 20g after 32 days, i.e. at t=32 M=20

The Gini index is calculated using the formula

where L(x) is the Lorenz curve. Inserting L(x) given in the question we find

Hence the correct answer D.

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

Now, the cost of building 2 units is

When the production increases to 4 units we get

To find the increase of the cost, we calculate the difference which gives