Exam 7: Matrix Algebra

Find the amount of each raw material the manufacturer will need to fill the orders.

Set up a matrix equation with integer values that is equivalent to the system of equations. -

A large oil company produces three grades of gasoline: regular,unleaded,and super-unleaded.To produce these gasolines,equipment is used which requires as input certain amounts of each of the three grades of gasoline.To produce a dollar's worth of regular requires inputs of worth of regular,$0.18 worth of unleaded,and $0.17 worth of super-unleaded.To produce a dollar's worth of unleaded requires inputs of $0.14 worth of regular, Worth of unleaded,and Worth of super-unleaded.To produce a dollar's worth of super-unleaded requires inputs of Worth of regular,$0.17 worth of unleaded,and $0.11 worth of super-unleaded.In addition,the oil company has final demands for each of the different grades of gasoline.Find the coefficient matrix that would be used in determining the total output of each grade of gasoline.

Look at the equations (a)Set up these equations in the matrix form Ax = b (b)Find (c)Using ,solve the equations.

If ,then

Solve the matrix equation: =

An appliance store has 25 refrigerators,30 ranges,and 10 dishwashers in stock,and a second store with 15 refrigerators,25 ranges,and 20 dishwashers in stock.If the value of each refrigerator is $600,each range is $300 and each dishwasher is $250,find the total value of the inventory at the two appliance stores.

What is the total demand for the four types of energy from only the energy industries?

The prices (in dollars per unit)for 3 video tapes are represented by the price vector: A video rental store orders these tapes in the quantities given by the column vector: Find the total cost (in dollars)of the purchase.

Find the income earned by the gas industry and its cost for the other forms of energy it uses.Then calculate its profit.

Solve by the method of reduction:

Find the total cost of raw materials for these vehicles.

(Use the matrix operations on a graphing calculator.)

Use the matrix operations on a graphing calculator to find the total demand for the four types of energy from only the consumers.

A boom in the economy causes an across the board increase of 10% in energy demands in the area.Calculate a new demand matrix which reflects this increase.

=

Use the encoding matrix an additional coding 1 matricx plus the matrices to answer the question. -4(E + 3I)

What would her income be if increasing it threefold would cause her profit to be five times as large? (Round to the nearest thousand dollars.)

Let A = ; find .

and