MTH302 Ass Sol

QUESTION # 1 Mark 08

A flying company offers trips in Europe. The company flies three kinds of airplanes: the Boeing 757, the Boeing 767, and the Boeing 777. Each plane is outfitted with tourist, economy, and first-class seats. In Boeing 757, there are 50 tourist, 30 economy, and 32 first class seats. . In Boeing 767, there are 75 tourist, 45 economy, and 50 first class seats.

In Boeing 777, there are 40 tourist, 25 economy, and 30 first class seats.

The number of reservations for its January flight to Germany, 305 reservations for tourist class, 185 Economy class, and 206 first class.

To fill all the seats how many of each kind of plane should the company fly?

SOLUTION
PLANES Eco. Class First Class Tourist
Boing 757 30*3=90 32*3=96 50*3=150
Boing 767 45*1=45 50*1=50 75*1=75
Boing 777 25*2=50 30*2=60 40*2=80
Reservations 185 206 305



To fill all the seats each kind of plane should the company fly:

Boing 757 3 Planes

Boing 767 1 Plane

Boing 777 2 Planes


QUESTION # 2 Marks 0

Why the inverse of following matrix is not possible?



SOLUTION

Because the number of rows and columns are not equal.

QUESTION # 3 Marks 0

Write all the steps which are necessary to calculate the inverse of following matrix in Ms Excel and then also write the inverse matrix of given matrix.



SOLUTION
Enter data in cells A1:C3.
Click on cell A4.
Keeping left mouse button pressed, drag it to cell C6.Four cells will be selected.
Press F2 from keyboard.
Type the formula =MINVERSE(A1:C3).This will appear in cell A4.
Press Ctrl, Shift, Enter keys simultaneously from keyboard.
Multiplicative inverse of the matrix will appear in cells A4,B4,C4 & A5,B5,C5 &

A6,B6,C6.

Inverse Matrix is:



0.059701 0.149254 -0.34328

0.099502 -0.08458 0.094527

-0.06468 0.004975 0.288557


QUESTION # 4 Marks 0


Discuss the importance of determinant of a matrix in evaluation of its inverse. Also state at least two properties of determinants which help in their evaluation.

SOLUTION


QUESTION # 5 Marks 0

Find amount of markup and selling price on an item that costs Rs. 2400 if there is a 40% markup on cost.



SOLUTION

Selling Price = Cost + (Cost * % Markup on Cost)

Markup = 2400 * (40/100) = Rs. 960

Selling Price = 2400 + 960 = Rs. 3360


QUESTION # 6 Marks 0


An item sells for Rs. 3200. If the markup on the cost is 48%, find the cost and the amount of the markup.


SOLUTION

Selling Price = Cost + (Cost * % Markup on Cost)

Selling Price = Cost + (1 + % Markup on Cost)

3200 = Cost + (1 + 0.48)

Cost = 3200/1.48 = Rs 2162

Markup = 2162 * (48/100) = Rs. 1037.76

QUESTION # 7 Marks 0

Find the single discount rate that is equivalent to the series discount of 5%, 7% and 11%.

SOLUTION

Let List Price = L = 100

Net Price = 100(1-0.05)(1-0.07)(1-0.11)

Net Price = 100 * 0.7863

Net Price = 78.63

Single Discount = 100 – 78.63 = 21.37%

QUESTION # 8 Marks 05

An item that cost Rs. 2300 was marked up 38 % of the selling price. After some time the item is markdown 30 %. Calculate the sale price after markdown.

SOLUTION

Let the selling price = 100

% markup on selling price = 38%

Cost = 100 – 38 = 62

Original sale price = (100/62) * 2300 = Rs. 3709.677

% markdown = 30%

Markdown = 3709.677 * 0.30 = Rs. 1112.903

Sale price after markdown = 3709.677 – 1112.903 = Rs. 2596.774
 

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