MTH302 ASSIGNMENT 1 SOLUTION 2021 | MTH302 ASSIGNMENT 1 FALL 2021 | MTH302 ASSIGNMENT 1 2021 | BUSINESS MATHEMATICS AND STATISTICS | VuTech

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Question No. 2

A school organized a book fair and in this book fair a bookseller is selling his books under the following rules:

There are three different packages available.

First package contains 2 Islamic books, 2 Science books and 2 Geography books, second package contains 2 Islamic books, 4 Science books and 1 Geography books and third package contains 3 Islamic books, 4 Science books and 5 Geography books. First package makes a profit of Rs. 120, second package makes Rs. 100 and third package makes Rs. 270 per pack.

How many packs should be made to maximize book fair profits? What will the profit be?

Solution:

First, we make 1^st package

2 Islamic Book = 125 * 2 = 250

Reminder Islamic Books = 0

2 Science Book = 125 * 2 = 250

Reminder Science Books = 50

2 Geography Books = 125 * 2 = 250

Reminder Geography Books = 20

We make 2^nd Package

2 Islamic Book = 75 * 2 = 150

Reminder Islamic Books = 100

4 Science Book = 75 * 4 = 300

Reminder Science Books = 0

1 Geography Book = 75 * 1 = 75

Reminder Geography Books = 195

 

We make 3^rd Package

3 Islamic Book = 54 * 3 = 162

Reminder Islamic Books = 88

4 Science Book = 54 * 4 = 216

Reminder Science Books = 84

5 Geography Book = 54 * 5 = 270

Reminder Geography Books = 0

So, we have

125 for First Package

75 for 2^nd Package

54 for 3^rd Package

Now, We derived profit.

Multiply package by the given prices

120 * 125 = 15000

100 * 75 = 7500

270 * 54 = 14580

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Question No. 3

You have been offered two deals for the car worth 1,600,000 that you’re purchasing.

Deal 1: Series discount of 3% , 5% and 7%.

Deal 2: A cash discount of 15/10 [i.e 15% discount if payment made in first 10 days].

Which deal will you choose and why?

Solution:

Deal 1

We know that formula for series discount

                        Net Price = L * 1 (1 – d₁) (1 – d₂) (1 – d₃)

                        List Price = 16,000,000

                        N = 16,000,000 * 1(1 - 3%)(1 - 5%)(1 - 7%)

                        N = 16,000,000 * 1(1 – 0.03)(1 – 0.05)(1 – 0.07)

                        N = 16,000,000 * 1(0.97)(0.95)(0.93)

                        N = 16,000,000 * 0.856995

                        N = 13,71,192

Deal 2

We know that formula for cash discount

                        N = L (1 - d)

N = 16,000,000 (1 – 15%)

N = 16,000,000 (0.85)

N = 13,60,000

So, we have

Deal 1 is N = 13, 71, 192

Deal 2 is N = 13,60, 000

So, the deal 2 is more beneficial for us.

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