Reference no: EM133246431

Question 1

a) An electronics store has 35 televisions, 15 VCRs, and 25 CD players in stock. If the value of each television is 400 eur, each VCR is 200eur and each CD player is l50eur. Use the matrix operations on a graphing calculator to find the total value of the electronics store's inventory.

b) Assuming the value of the goods ln question (a) remains constant, what would be the new value of the inventory if the store had to buy an additional 16 televisions, 10VCRs, and 18 CD players?

c) The price charged for 2 different CDI at two different stores can be represented by the matrix r The quantities of each CD sold at each store can be represented by the matrix Q.  Show that the transpose of the income generated T is equal to the product of the transposes of P and Q ln reverse order,Q^T,T

Question 2

a) Reduce the augmented coefficient matrix of the following system (using Guass Jordan elimination method)

6A + B + 3C = 35

3A + 2B + 2C

22A + 5B + 3C = 18

b) Show that by using Cramer'S rule and the Guass Jordan elimination method one gets the same result for x, y, and z.

Question 3

a) Using integration by parts, solve the following integral:

J e^x 2dv

b) A marginal revenue function for a product is given by:

dr/ d, - 1700 + q(3 q' - q)

If r is the total revenue function in euro, using the Fundamental Theorem of Integral Calculus, find the additional revenue generated when increasing production from 40 to 45 units.

c) The demand function for a product is given by:

p -- D q) -- 8 - 0.01q

The supply function for the same product is given by:

p = A(q) = 0.003q'

where p is the price in euro per unit q when q units are supplied or demanded.

i) Find the points of market equilibrium

ii) Using definite integration, find the consumers' and producers' surplus under market equilibrium

Question 4

Using integration by substitution work out the following:

₁∫² 3xe² dx

A machine's value depreciates 25% in the first year since it's purchase. The rate at which it subsequently depreciates is proportional to its value.

Suppose that such a machine was purchased new on June 1" 2005 for C40,000 and was valued at €19,450 on June 1" 2016.

i) Determine a formula that expressed the value Sof the machine in terms of r, the number of years after June 1st 2005.

ii) Using the formula in b(ii) determine the year and month which the machine will have a value of C15,000.

Attachment:- Sample Maths.rar