1. ## MTH302 Business Mathematics & Statistics Assignment 2

Due date: 17-05-10

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Question 1: Marks 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?

Question: 2 Marks 0

Why the inverse of following matrix is not possible

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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.

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.

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.

Question 7: Marks 0

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

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.

2. Solution

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For an inverse of Matrix it is necessary the number of rows must be equal to number of rows. In this matrix number of rows are 4 & number of Column are 3. so it is not possible the inverse of give matrix.

1-Write the value of first column in cell 5 in A: 4, 7 in A: 5 and 1 in A: 6
2-Simlarly the value 2nd Column will be written 9 in B: 4, 1 in B: 5 and 2 in B: 6
3-Finally the value of 3rd column will put as 3 in C: 4, 8 in C: 5 and 4 in C: 6
4-Click the cell A: 7 and drag the mouse keeping press left button of Mouse to C: 9
5-Then press F2 in A: 7 and write the formula =MINVERSE (A: 4: C: 6)
6-After writing formula Press CTR+SHIFT+ENTER keys simultaneously the formula will appear in formula as {=MINVERSE (A: 4: C: 6)} which shows that job has been done in correct manner.

Selling price = Cost+ (cost * % of mark up)
=2400+ (2400*.4)
=2400+960
=3360
So the mark up is =960
Selling price =3360

First we calculate the Markup

Mark up =% age of mark up * Selling Price
=.48*3200=1536
Now the cost
Price is = Selling Price-Mark Up
=3200-1536=1664

Equivalent Discount Rate = (1-d1) (1-d2) (1-d3)
= 100(1-5%) (1-7%) (1-11%)
=100(.95)(.93)(.89)
=78.63
% Discount =100-78.63
=21.37%

Selling Price = Cost+(Cost*%of Mark Up)
=2300+(2300*.38)
=2300+874
=3174

Selling Price after mark down =Selling price-(selling price*%of mark down)
=3174-(3174*.30)
=3174-952.20=2221.80

Solution: Here, there are two parts to this problem. first we must find the original sale price so that markdown can be calculated on that price.

[U]original sale price:
Let Selling price=100
%markup on selling price=38%
cost= 100-38=62
thus original sale price=(100/62)x 2300=3709.67Rs

Rs. Markdown:
%markdown=30%=0.3
Rs. markdown= 3709.67x 0.3=1112.901

Sale price after markdown:
Sale price after mark down=3709.67-1112.901=2596.76Rs.