math problems ma_u4_a2

Exercise 3 . Total revenue function from marginal revenue .

A department store has marginal revenue in the perfumery department according to the following function:



x represents the number of items sold per month perfumery department .

Determine the function representing total revenues.
 

solution:
As we get marginal revenue need to calculate the integral for the total income we have :

I ( x ) = I '(x ) = 28x3 - 14x dI = dx ( x4 -x2 ) 3 = 74x3 -2x dx ( x4 -x2 ) 3

To solve the integral we use the technique of integration by substitution , with what we have :
= -x2 or x4
du = (4x3 -2x ) dx
The integral is complete continue with the replacement of the variable u being as follows:

I ( x ) dx = -2x 74x3 ( x4 -x2 ) 3 = 7duu3

Now we just have to solve the integral 7duu3
Ente case to solve the integral variable u spent with exponent in the numerator of opposite sign , being the expression as follows :

I ( x ) = 7u - 3du

Now performing the integration we have:

I ( x ) = 7 u- 3 +1 +1-3 + C = , 7u , 22 + C

Now returns the variable u in the denominator , changing the sign of the exponent with what we have again :

I ( x ) = - 72u2 + C

The last step is to change the variable u by its value against ax with what you have :
I ( x ) = -72 ( x4 -x2 ) 2 + C

By not selling no income so the constant of integration is zero so that we have:

I ( x ) = -72 ( x4 -x2 ) 2

Therefore the function representing total revenue from the sale of perfume per month are:

I ( x ) = -72 ( x4 -x2 ) 2



conclusion :
The use of integrated economic - administrative area are important because they may have applications in the calculation of total income , in whole or calculate the total income that causes any selling, in this case perfume cost and gives the following function

: I ( x ) = -72 ( x4 -x2 2)


 



Exercise 4 . Concept application in financial mathematics

Relate the functions of the left column with the correct answer in the right column :
 
(6 )
Represent stocks of any article, material or resource used in an organization for the manufacturing and / or distribution .
1. Resource depletion .
( 1)
It occurs when revenues are lower than the costs of the company profits are lost and starts .
Two . Capital Cost .
(10 )
Are the elements of material, technological or human character used to perform a specific task which is to reach a final goal.
3 . Operating cost .
( 9)
Allows the company's business efficiently and going from the area of process machinery to computers from the office area .
April . Maintenance costs.
(5)
It is the process by which continuously accumulated amount of capital increases and is a function of time .
May . Capital formation.
( 4)
Are generated by having an item in stock , they include capital costs invested deterioration , obsolescence, theft, tax and insurance , as well as space, equipment , depreciation of the building and warehouse equipment , etc. .
6. Inventory.
( 2)
Is purchase cost minus the salvage value .
7. Human resources.
( 8)
Lets spend the amounts of money for various activities such as payments , purchases , wages, among others.
8. Resource material.
( 3)
Includes cost of ownership and maintenance .
9. Technological resource .
( 7)
Applies staff available to the company or enterprise to carry out activities with the support of technology resources.
10. Resources .


  conclusion :
The concepts used in the administration , material and human resources, technological resources, capital cost , operating cost, maintenance cost, capital formation, inventories , resource depletion are of elemental importance , showing data generated using the resources and costs you have an organization and we show that both a company worth determined by the use of its resources.