1. Sigma Mathematics Workbook © Pearson Education New Zealand 2007 x y A B C D E 12.05 The diagram below shows a feasible region. It is drawn to scale but there is no information about the values of the coordinates. a At what point is the value of 5x + 6y a maximum? b At what point is the value of x – 4y a minimum? a 5x + 6y takes the value k. Rewrite in gradient-intercept form: Represent this combination by a line.5x + 6y = k Draw a line with gradient somewhere inside the feasible region and move it outwards

2. Sigma Mathematics Workbook © Pearson Education New Zealand 2007 12.05 The diagram below shows a feasible region. It is drawn to scale but there is no information about the values of the coordinates. a At what point is the value of 5x + 6y a maximum? b At what point is the value of x – 4y a minimum? x y A B C D E a 5x + 6y takes the value k. The sequence of parallel lines escapes the feasible region after C. 5x + 6y is a maximum at C as C gives the largest possible y-intercept. 5x + 6y = k Make k as large as possible i.e. the y-intercept as large as possible

3. Sigma Mathematics Workbook © Pearson Education New Zealand 2007 x y A B C D 12.05 The diagram below shows a feasible region. It is drawn to scale but there is no information about the values of the coordinates. a At what point is the value of 5x + 6y a maximum? b At what point is the value of x – 4y a minimum? b x  4y takes the value k. Rewrite in gradient-intercept form: Represent this combination by a line. x  4y = k E

4. Sigma Mathematics Workbook © Pearson Education New Zealand 2007 12.05 The diagram below shows a feasible region. It is drawn to scale but there is no information about the values of the coordinates. a At what point is the value of 5x + 6y a maximum? b At what point is the value of x – 4y a minimum? Make k as small as possible, ie the y-intercept should be as large as possible (notice the effect of the negative sign). b x  4y takes the value k. x  4y = k x y A B C D E

5. Sigma Mathematics Workbook © Pearson Education New Zealand 2007 12.05 The diagram below shows a feasible region. It is drawn to scale but there is no information about the values of the coordinates. a At what point is the value of 5x + 6y a maximum? b At what point is the value of x – 4y a minimum? Make k as small as possible, ie the y-intercept should be as large as possible b x  4y takes the value k. x  4y = k Draw a line with gradientsomewhere inside the feasible region and move it outwards x y A B C D E

6. Sigma Mathematics Workbook © Pearson Education New Zealand 2007 x y A B C D 12.05 The diagram below shows a feasible region. It is drawn to scale but there is no information about the values of the coordinates. a At what point is the value of 5x + 6y a maximum? b At what point is the value of x – 4y a minimum? Make k as small as possible, ie the y-intercept should be as large as possible b x  4y takes the value k. x  4y = k The sequence of parallel lines escapes the feasible region after A. x – 4y is a minimum at A. E