MTH3: HIRE PURCHASE AND LINEAR PROGRAMMING

This unit is about hire purchase since most people do not have enough money to buy expensive things they tend to use hire purchase to get those things, Linear programming.

HIRE PURCHASE

Very often people do not have enough money to pay cash for expensive items. With hire purchase the customer pays a down payment for the item, acquire the item and pay the remaining money in equal installments for a given period of time.

For example

A calculator costs 12,000/= for one paying cash. If it is bought under hire purchase one pays a deposit of 40% of cash price and 4 weekly installments of 2500/= each. Calculate.

  1. the hire purchase price.
  2. the extra amount paid over the cash price expressed as a percentage.

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a)A pick up wan can be bought by cash at Shs. 8,750,000 or can be brought on hire purchase by paying a 25% deposit of the cash price at 12 monthly installments of Shs. 600,000 per month. Calculate the

  1. i) cost of the pick up by hire purchase
  2. ii) extra money paid for the pick up by hire purchase than by cash.

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  1. The following is an advertisement of a canon photocopier

GET YOURSELF A PHOTOCOPIER CHEAPLY WHILE STOCK LAST!!

TERMS: CASH AT 960,000/=

OR HIRE PURCHASE; DEPOSIT 15% OF MARKED PRICE AND PAY EITHER USHS 75,000/= WEEKLY FOR 12 MONTHS OR USHS 245,000 MONTHLY FOR 4 MONTHS.

Calculate;

  1. The saving a customer would make by buying the photocopier on cash terms rather than the weekly hire purchase.
  2. Cash terms = 960,000/=

Hire purchase

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  1. The percentage profit made on the monthly hire purchase if the whole sale , cost of a photocopier is A.5% below he cash price.

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Example
Find the coordinates of the image A1 of A (-2 , 4)after reflection in the line y= -x

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Transformation matrix for rotation in the anti clockwise direction is positive while negative in the clock wise direction.

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Show that the image of (1,0)under a rotation of+30 about the origin is

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ii) Write down the coordinates of the images of (1,0) and (0,1) under the transformation of M^2 and explain your answer geometrically.

A VIDEO BELOW SHOWS HOW TO SOLVE PROBLEMS WITH HIRE PURCHASE

LINEAR PROGRAMMING
An manufacturer makes to types of hoes A and B. The following conditions apply to daily product.
Each type of A Costs shs. 3000 and each type of B costs sh. 5000 and the manufacturer has a maximum of shs. 450,000 available.
Due to labour shortage the production of type A plus four times that of B 160.
A study of the market recommended that the number of type B produced should not exceed twice the number of type A Produce.

a) Given that x hoes of type A and y hoes of type B are made. White down three in equalities a part from x ≥ 0, y ≥ 0, satisfying the above conditions.
b) Show graphical the region containing the points satisfying the above conditions.
c) Taking x+2y as a suitable expression for the manufacturers’ profit find the number of each type of hoe that should be made to obtain the greatest profit.
Soln.

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Let x represent 8 tonne lorry let y represent 10 – tone Lorries
Let y represent 10- tone Lorries

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ii) plot these inequalities . on the same axis , state out the unwanted region.
Find the number of 10 tonne and 8. Tone lorries the company used, keep its costs as
minimal as possible. (0,0) 40,000 x 0 + 60,000 x 0 =0

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2. A wildlife club in a certain school wishes to go for on excursion to a national park. The club has hired a minibus and a bus to take the students. Each trip for the bus is shs. 50,000 and that of a minibus of 54 students and the mini-bus 18 students. The maximum of students allowed to go for the excursion is 216. The number of trips the bus makes do not have to exceed those made by the minibus.
The club has mobilized as much as sh. 300,000 for transportation of students. If x and y made by the number of trips made by the bus and mini- bus respectively.
i) Write down five inequalities representing the above information.

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  1. Plot these inequalities on the same axes.
  2. By shading the unwanted region show the region satisfying all the above inequalities.
  • List the possible number of trips each vehicle can make.

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3. A school lorry and a school bus are to be used to transport students to a certain function.
The capabilities of the lorries and the bus are 50 and 70 students respectively. The number of students to attend the function should not exceed 350. Each trip made by the lorry or the bus cost shs. 3,000. The money available for the transportation is sh. 18.000.
The number of trips made by the lorry should not exceed that made by the bus. If x and Y are the number of trips to be made by the lorry and bus respectively.
i) Write down five inequalities respectively this information.
ii) Plot these inequalities on the same axes.
iii) By shading the unwanted region show the region satisfying all the inequalities.
iv) If all the available money for transport is to be used , list all possible number of trips that each vehicle will make.
(Assume vehicle is full for each trip)
v) Find the greatest number of students that can be transported.

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in a certain school teachers salary includes the following tax-free allowances;

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Mr. Mugisha and Ofuti are senior teachers in this school. Mr. Mugisha married with two children under 10 years and one above 10 years. He is also a class teacher and Head of math department. Mr. Ofuti is single but has two children less than 10 years and is also a house master and a class teacher. Their gross incomes at the end of the month are each subjected to “PAYE” (pay as you earn) which have the following rages.
For the first sh. 10,000 taxable incomes is 20% while the rest is taxed at 15% at the end of the month Mr. Mugisha’s gross income was sh. 150,000 and Mr. Ofuti’s gross income sh. 130,000.

Calculate the
a) Taxable income for each teacher.
Mr . Mugisha
Allowances

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Taxable income
130,000-12,500
=117,500/=
b) Tax paid by each teach
A VIDEO ABOUT LINEAR PROGRAMMING SOLUTIONS

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ASSIGNMENT : HIRE PURCHASE AND LINEAR PROGRAMMING ASSIGNMENT MARKS : 20  DURATION : 2 hours

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