# Form 4 Mathematics Linear Programming Questions and Answers

In this session, we are going to solve several questions on linear programming, a from 4 mathematics topic. Solutions are available in video format. All questions are exam standard and suitable for those preparing for KCSE exams.

Lessons (**16**) * SHARE*

- 1.
At an agricultural research station a rectangular plot is to be allocated for a certain experiment. The length of the plot must be greater than the breadth but not more than twice the breadth. The area must be more than #400m^2# and the perimeter must be less than 200m. (a).Form inequalities representing the above information and graph them on the grid provided

12m 18s - 2.
A trader stocks two brands of rice A and B. The rice is packed in packets of the same size. The trader intends to order fresh supplies but his store can accommodate a maximum of 500 packets. He orders at least twice as many packets of A as of B. He requires at least 50 packets of B and more than 250 packets of A. If he orders x packets of A and y packets of B,

9m 51s - 3.
A carpenter takes 4 hours to make a stool and 6 hours to make a chair. It takes the carpenter and at least 144 hours to make x stools and y chairs. The labour cost of making a stool is Ksh 100 and that of a chair is Ksh 200. The total labour cost should not exceed Ksh 4 800. The carpenter must make atleast 16 stools and more than 10 chairs. (a) Write down inequalities to represent the above

12m 43s - 4.
A company is considering installing two types of machines. A and B. The information about each type of machine is given in the table below. The company decided to install x machines of types A and y machines of type B (a) Write down the inequalities that express the following conditions
I. The number of operators available is 40 II. The floor space available is #80m^2#

14m 19s - 5.
Mwanjoki Flying Company operates a flying service. It has two types of aeroplanes. The smaller one uses 180 litres of fuel per hour while the bigger one uses 300 litres per hour.The fuel available per week is 18 000 litres. The company is allowed 80 flying hours per week. To keep the aeroplane in good condition the bigger aeroplane must be flown for x hours per week while the smaller aeroplane

9m 40s - 6.
A transporter has two types of trucks to transport sugar.types A truck carries 2,000 bags while type B carries 3,000 bags per trip.The transporter has to transport 120,000 bags. He has to make not more than 50 trips.Type B trucks are make at most twice the number of trips made type A (B to be at most twice A). (a)By taking x to be the number of trips made by type A trucks and y to be the number

9m 28s - 7.
A coffee merchant has 400kg of Robusta coffee and 480kg of Arabica coffee. The coffee is packaged by weight as follows: Type I: 30% Robusta and 70% Arabica Type II: 50% Robusta and 50 % Arabica Type I is sold at sh.34 per kg while type II is sold at sh.36 per kg. Use graphical method to determine the number of kilograms of type I and type II which should be packaged to maximize the profit.

12m 38s - 8.
A school has to take 384 people for a tour. There are two types of buses available, type X and type Y. Type X can carry 64 passengers and type Y can carry 48 passengers. They have to use at least 7 buses (a) Form all the linear inequalities which will represent the above information. (b) On the grid provided, draw the inequalities and shade the unwanted region.

9m 25s - 9.
A factory manufactures two product which are produced on three machines X, Y and Z. The first product requires 2 hours on machine X, 3 hour on machine Y and 1 hour on machine Z. The second product requires 1 hour on machine X,4 hours on machine Y and 2 hours on machine X can be used for at most 100 hours, machine Y for at most 240 hours and machine Z for at most 90 hours

13m 43s - 10.
A manufacturer of jam has 720 kg of strawberry syrup and 800kg of mango syrup for making two types of jam, Grade A and B. Each type is made by mixing strawberry and mango syrup as follows: Grade A: 60% strawberry and 40% mango. Grade B: 30% strawberry and 70% mango. The jam is sold in 400 gram jars: The selling prices are as follows: Grade A: Sh.48 per jar. Grade B: Sh.30 per jar.

13m 43s - 11.
An institute offers two types of courses: Technical course and business course. The institute has a capacity of 500 students. There must be more business students than technical students but at least 200 students must take technical courses. Let x
represent the number of technical students and y the number of business students. a).Write three inequalities to represent the given information.

6m 2s - 12.
A draper is required to supply two types of shirts, type A and type B. The total number of shirts must not be more than 400.He has to supply more of type A than type B. However the number of type A shirts must not be more than 300 and type B shirts must not be less than 80.Let x be the type A shirt and y b e the type B shirts. i).Write down all the inequalities representing the information.

6m 19s - 13.
A theatre has a sitting capacity of 250 people. The charges are sh.100 for an ordinary seat and sh.160 for special seat. It costs sh.16, 000 to stage a show and the theatre must make a profit.There are never more than 200 ordinary seats and for a show to take place at least 50 ordinary seats must be occupied. The number of special seats is always less than twice the number of ordinary seats.

10m 32s - 14.
Bot juice company has two types of machines,A and B,for juice production.Type A machine can produce 800 litres per while type B can produce 1600 litres per day.Type A machine needs 4 operators and type B needs 7 operators. At
least 8000 litres must be produced daily and the total number of operators should not exceed 41.There should be 2 or more machines of each type.

9m 42s - 15.
The dimensions of a rectangular floor of a proposed building are such that: -the length is greater than width but at most twice the width. The sum of the width and the length is,more than 8m but less than 20m,If x represents the width and y the length. a).Write inequalities to represent the above information. b).i).Represent the inequalities in part (a) above on the grid provided.

8m 7s - 16.
Omondi makes 2 types of shoes: A and B. He takes 3 hours to make one pair of type A and 4 hours to make one pair of type B. He works for a maximum of 120 hours to make x pairs of type A and y pairs of type B. It costs him sh.400 to make a pair of type A and sh.150 to make a pair of type B. His total cost does not exceed sh.9000.He must make 8 pairs of type A and more

12m 58s

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