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Midterm of MTH302 - BUSINESS MATHEMATICS & STATISTICS

Paper patron of MTH302 - BUSINESS MATHEMATICS & STATISTICS

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3- Attempt all the questions on one Excel Worksheet (use only sheet 1) to solve all

the questions. More than one sheet is not acceptable. If you solve any question on

sheet2, sheet3 and so on, it will not be graded.

4- Solve the questions on excel worksheet in usual manner i.e. from upward to downward

not from left to right.

5- Variables (say x, y, and z) are given in the questions you can assign any value to variable

within the range mentioned in the questions.

(e.g. A man sells shirts of Rs x and he gets a profit of 10%. Then find the profit. (25000<30000)

Solution: Here we can take x as any value between 25000 to 30000.

Take x = 26000

Profit = 26000*10/100 = 2600 Rs Answer

Or

Take x = 26500

Profit = 26500*10/100 = 2650 Rs Answer )

6- Attempt all questions. Marks are written adjacent to each question.

7- Do not ask any questions about the contents of this examination from anyone.

If you think that there is something wrong with any of the questions, attempt it to the best

of your understanding.

If you think that some essential piece of information is missing, make an appropriate

assumption and use it to solve the problem.

8- Write all steps, missing steps may lead to deduction of marks.

9- The main restriction for Take Home Exams is that it must be your own work–you must

attempt it by yourself without any outside help. You can't copy chunks of text directly from

textbooks or notes. This counts as plagiarism.

10- If you do not solve paper on Excel Sheet, you will get a zero mark. So paper on Word

files or any format other than Excel will not be graded.

**WARNING: Please note that Virtual University takes serious note of unfair means.

Anyone found involved in cheating shall get an `F` grade.

For Teacher's use only

Question 1 2 3 4 Total

Marks

Question No: 1 ( Marks: 25 )

Things to remember

Successive Discount is the discount which is calculated on the previously discounted value.

Cash Discount is the discount offered by an agreement in favor of returning the credit in

time.

In the marketing chain described in lectures, there are more than one person between the

manufacturer and the end user. Let us define this chain as

Manufacturer Distributor Wholesaler Retailer Buyer

Suppose you are CEO of a manufacturing company of plastic canes, bottles, and boxes and being

CEO, you have to take all the decisions. Today, you have received an order of x units from one of

your regular clients. You have to consider operating expenses, Gross profit, and depreciation

allowance of the assets. (990<1010)

To carry out this order you buy raw material costing Z and by agreement after paying 20% in cash

if rest of the amount will be paid within 20 days of delivery, you will get 3% discount. If you delay

it you will be liable to pay 14% annual interest on the amount you were liable to pay. Suppose, the

whole product you sell as a retailer is making more net profit of 5% (more than expected) on sale

price. (1000000<1200000)

Since, you as a manufacturer cannot directly approach to end user you have to follow marketing

chain described above.

Each identity in the marketing chain excluding you (Manufacturer) in the year2006, assigns the

mark up rates i.e. 6%,7%,8% by the distributor, wholesaler and retailer respectively on their cost.

This year, the default change in markup rates will be same as done by you (i.e. 10% explained

later). But each identity in marketing chain is also adding its own markup on its last year’s selling

price. Let this markup uniform for each as 2% i.e. a total of 12%.

Your product available in a large quantity at one of your outlets is troubling you as a Retailer. Then

you decide to carry out successive discounts with specific time intervals. During the first week, the

discount rate was 9% on the tag price. During the second week, it was 12% and then 18% in third

week.

a) Now separately assign each expense a certain percentage not exceeding 20%. Last year

average sale price of product was Y rupees per unit which could be 10 % more than this

year as markup due to the increased goodwill of your company. Calculate each expense on

the increased sale price. Find the sale price that you will offer as manufacturer. (65<75)

b) If you deposit the amount you were liable to pay for raw material with net profit you earned

as Retailer into a saving account which pays 13% annual interest. Whether the amount

should be returned now or deposited for 10 years? Construct the data properly defining

each step then justify your answer logically.

c) Formulate the sale prices offered by each identity in marketing chain for the year 2006 and

2007.

d) Since you have obtained the list price as a Retailer find the sale price after successive

discounts weekly. If the rates are considered as series discounts, then find single discount

rate that is equivalent to the series. Also find the net price of the unit at that rate considering

the original retailer’s price.

Question No: 2 ( Marks: 5 )

Sub scenario

Being the owner of this manufacturing plant you have a complete hierarchy of employees

consisting of MD (Managing Director) 3 Supervisors and 21 skilled laborers. You can pay only

30% of the profit as salaries of your employees. The profit you earned is supposed to be Z. If the

gross salary of the skilled labor is x, which of supervisor is two times than that of laborer and that

of MD is three times than that of laborer. Calculate the Gross salary of each of the person working

at your plant. Formulate complete pay roll i.e allowances and benefits that you will offer.

(1000000<1200000)

Question No: 3 ( Marks: 5 )

You took a loan of L and have to pay it off at 12% annual interest rate in payments of 12 years.

First, calculate the payment per period at the end of each period. Now when you pay it back with

interest in this manner, you will be paying a certain part of Principal amount as well as interest at

each payment. Here you are required to find interest and principal amount paid at each payment

period. Show it in columns and in the end find the cumulative interest and principal you paid. Keep

this thing in mind that the entity that gives you loan will take interest at the outstanding loan after

each period. (200000<210000)

Question No: 4 ( Marks: 10 )

Five diabetic patients in a hospital each require three kinds of insulin injections each day. The

amount of the 1st kind of insulin given to five patients is 10 units, 40 units, 30 units, 20 units and

10 units respectively. The amount of the 2nd kind of insulin given to five patients is 20 units, 20

units, 10 units, 10 units and 10 units respectively. The amount of the 3rd kind of insulin given to

five patients is 30 units, 5 units, 5 units, 20 units and 10 units respectively. If patient 1 plans to stay

x days, patient 2 stays 3x days, patient 3 stays 2x days, patient 4 stays x days, and patient 5 stays x

days. (5<11)

Find the matrix made by insulin of 5 patients and calculate its inverse if possible. How much of

each type of insulin must the medical staff have on hand?

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