Task 1: Optimisation using GeoGebra [30 marks] An optimisation problem in x and y is described as follows. Minimise C = 5x - 2y It is subject to several constraints (also called inequalities). (1a) Finding and drawing the constraints (also called inequalities) and showing all the vertices of the Feasible Region You need to find and draw each constraint using GeoGebra. See information about how to draw them in part (iii) and part (iv). (i) Find the 1st constraint [2 marks: correct answers only] The line passes through A (6, 7) and B (12, 12) and the rejected region shaded out is above the line, so the point (0, 0) belongs to this constraint (it is not in the shaded region). (ii) Find the 2nd and the 3"d constraint [2 marks: correct answers only] The values of x cannot be more than 12 (2"d constraint). The values of y cannot be more than 16 (3"d constraint). The other constraints to which this problem is subject are: 5x + 2y 2 44 (4th constraint) 2y 2 x - 4 (5th constraint) 4zy - x (6th constraint) Note: One of the constraints may be redundant. (iii) Draw each constraint with GeoGebra by selecting the following object properties: . Colours: 1st one in black, 2nd one in red, 3"d one in orange, 4th one in green, 5th in brown and 6th constraint purple [3 marks: -1 per mistake, minimum 0] Style: Line Thickness of 1, Filling using hatching and inverse filling (so shading the area we do not want), with an angle of 0 and spacing of 20. [8 marks: 2 marks per feature, for each one -1 per mistake, minimum 0] . Basic: The labels in the graph have to show the constraints. [3 marks: -1 per missing constraint as label, minimum 0]Task 1: Optimisation using GeoGebra [30 marks] An optimisation problem in x and y is described as follows. Minimise C = 5x - 2y It is subject to several constraints (also called inequalities). (1a) Finding and drawing the constraints (also called inequalities) and showing all the vertices of the Feasible Region You need to find and draw each constraint using GeoGebra. See information about how to draw them in part (iii) and part (iv). (i) Find the 1st constraint [2 marks: correct answers only] The line passes through A (6, 7) and B (12, 12) and the rejected region shaded out is above the line, so the point (0, 0) belongs to this constraint (it is not in the shaded region). (ii) Find the 2nd and the 3"d constraint [2 marks: correct answers only] The values of x cannot be more than 12 (2"d constraint). The values of y cannot be more than 16 (3"d constraint). The other constraints to which this problem is subject are: 5x + 2y 2 44 (4th constraint) 2y 2 x - 4 (5th constraint) 4zy - x (6th constraint) Note: One of the constraints may be redundant. (iii) Draw each constraint with GeoGebra by selecting the following object properties: . Colours: 1st one in black, 2nd one in red, 3"d one in orange, 4th one in green, 5th in brown and 6th constraint purple [3 marks: -1 per mistake, minimum 0] Style: Line Thickness of 1, Filling using hatching and inverse filling (so shading the area we do not want), with an angle of 0 and spacing of 20. [8 marks: 2 marks per feature, for each one -1 per mistake, minimum 0] . Basic: The labels in the graph have to show the constraints. [3 marks: -1 per missing constraint as label, minimum 0]