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Catholic College Bendigo

Unit 2 General Maths (Further)2013 Linear Programming Test

Name:______________________ Time Allowed: 45 minutes Total Marks: ____/ 38 = ___%

Section A – Multiple Choice (6 x 2 = 12 marks)

Question 1: Which of the following statements is not true?

A -4 ≥ -7B 3 ≤ 3C 6 > 0D -1 ≥ 1E 12 < 13

Question 2: The lines of x+2 y=10 and 6 x+4 y=36 intersect at the point:

A (-4, -3)B (4,3)C (-3,-4)D (3,4)E They do not intersect

Question 3: The graph represented below has the required region not shaded. The inequality that is being represented is:

A 5 x+2 y<20B 5 x+2 y ≤20C 5 x+2 y>20D 5 x+2 y ≥20E 2 x+5 y>20

Question 4: The three inequalities below form a feasible region.

x≥0 y ≥0 y← 4 x+13

Which of the following points lie within the feasible region?

A (5,1)B (-4, 13)C (1,-4)D (2,5)E (1,6)



The following information is required for Questions 5 and 6.

A dressmaker makes two different types of dresses: short party dresses and long length formal dresses.

To make a party dress 3m of fabric is needed. The time taken make a party dress is 7 hours To make a formal dress 5m of fabric is needed. The time taken to make a formal dress is 5

hours. The dressmaker has 620m of fabric available and 800 hours of worker time to make the

dresses Let p represent the number of party dresses made Let f represent the number of formal dresses made

Question 5: The inequation which represents the constraint of fabric available to the dressmaker is:

A 3 p+5 f ≤620B 3p+5 f ≥620C 7 p+5 f ≤800D 7 p+5 f ≥620E 3 p+5 f ≤800

Question 6: The feasible region for the dressmaker is shaded below. The profit can be calculated by P=12 p+16 f .

How many party dresses ( p ) should she make to maximise her profit?

A 0B 45C 114D 207E It is impossible to tell



Section B - Short Answer (16 marks)

Question 1: On the axes below draw the graphs of: (Make sure you label any intercepts and include a key for the required region)

a) x>−4 b) 3 x−4 y≤24

(2 + 3 = 5 marks)

Question Two: The graph of y= x2+6 and y+2 x=10 are drawn below.

a) Find the co-ordinates of the point of intersection of the two graphs.

(1mark)b) On the graph indicate the region which satisfies the

following:

y ≤ x2+6 and y+2 x≥10

(1 mark)



Question 3: Draw the following inequalities on the axes below. Show the co-ordinates of all intercepts and points of intersection as well as the required region.

x≤4 y≥2 y≤3 x+1

(4 marks)

Question 4: In a linear programming problem the number of items that can be produced by a business in one day is shown below. (The feasible region is shaded)

a) On the graph above identify the co-ordinates of the corner points of the feasible region.(2 marks)

b) What is the maximum value for Z=0.5 x+2 y?



(2 marks)c) What are the co-ordinates where the value for Z is maximised?

(1 mark)

Section C – Application (10 marks)

Following a Natural disaster, the Army plans to use helicopters to transport medical teams and their equipment into remote areas. They have two types of helicopters: Redhawks (x) and Blackjets ( y ).

Redhawks can carry 45 people and 3 tonnes of equipmentBlackjets can carry 30 people and 4 tonnes of equipment

At least 450 people and at least 36 tonnes of equipment need to be transported.

Question 1: The constraints for the equation are x≥0 and y ≥0 as well as the constraints on the number of people and the amount of equipment that can be carried. State the constraints of:

a) the number of people transported

b) the amount of equipment transported

(1 + 1 = 2 marks)

Question 2: The feasible region of the problem is shown on the graph below.

a) Fill in the missing information.

(3 marks)

b) Add a key to indicate the required region.

(1 mark)

The cost of operating a Redhawk is $3600 per hour and Blackjets cost $3200 per hour to run.

Question 3: The objective function is given by C= x+¿ y, where C is the cost per hour. Fill in the missing information.

(1 mark)



Question 4: How many Redhawks and how many Blackjets should be used to minimise the cost per hour (C), and what is this cost?

(3 marks)

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