VCE General Maths (Further) Unit 2

Linear Programming

2014 Test

Name: _______________________________

Total: / 34 marks ( %)

Conditions: 45 min, Casio Calculator and Double sided handwritten Summary Sheet permitted

Section A-Multiple Choice (5×2=10Marks)

1. The x intercept of the line 3 x+ y=6 is:

A. (3,0) B. (−2,0) C. (2,0) D. (0,2) E. (0,6)

2. The point of intersection between the two lines 3 x+ y=5 and y=2x is:

A. (2,1) B. (1,2) C. (3,1) D. (2 ,−1) E. (0,5)

3. The equation of the line displayed is:

A. 4 x+5 y=4

B. 4 x−5 y=4

C. 5 x+4 y=20

D. 4 x+5 y=20

E. 4 x−5 y=20

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

A. x>4B. x<4C. y ≤4D. y<4E. y>4

Region required

5. The region required for a system of inequations is given by the graph below. If the profit (in dollars) is given by P=5 x+3 y, the maximum profit is:

A. $6B. $8

C. $22

D. $30

E. $32

Section B-Short Answer (Show ALL working) (24 Marks)1. Graph each of the following inequalities on the axes below.

(Label the coordinates of all intercepts and include a key for the required region.)

a. x<3 b. 2 x−3 y≥12

(2+3=5 marks)

(2,4)

Region required

2. On the set of axes below, graph the following system of linear inequations.Make sure you label the feasible region and label the coordinates of each corner point.

x≥0y ≥0

2 x− y≤12x+ y≤9

(5 marks)

3. Jane is concerned about her vitamin intake. Her doctor told her that she should try to get at least 150 units of vitamin A and 250 units of vitamin B from her cereal each week. The number of vitamin units in two different brands of cereal is shown in the table below.

Vitamin A Vitamin BBrand X 30 units per serve 25 units per serveBrand Y 10 units per serve 50 units per serveMinimum units required. 150 units per week 250 units per week

Let x be the number of serves of Brand X and y be the number of serves of Brand Y.a. From the table above we can write down two inequations to represent the vitamin

constraints, one for vitamin A and another for vitamin B.

The inequation for vitamin A is: 30 x+10 y ≥150

Write down the inequation to represent the vitamin B constraint. Label this equation 2.

There are a further two constraints below that may be described as obvious. x≥0y ≥0

Label these inequations 3 and 4

b. Graph the four inequalities below and label the feasible region.

c. If Brand X costs 75 cents per serve and Brand Y costs 90 cents per serve write the objective function for the total cost, C of purchasing x serves of Brand X and y serves of Brand Y.

d. Find the minimum cost each week to meet her vitamin requirements.

e. How many serves of each brand should she eat each week to meet her vitamin requirements for minimum cost?

(1+4+1+2+1=9 marks)