Answer: (e) (i) To represent the inequalities graphically on a coordinate plane, you can use a scale of 2cm to represent 5 units on each axis. To shade the unwanted regions, you can start by drawing the coordinate plane and labeling the x and y axes. Then, you can graph the inequalities by plotting the lines and shading the regions that do not satisfy the inequalities.
(b) 2x + 3y ≤ 30
This inequality represents a line with the equation 2x + 3y = 30. You can graph this line by plotting a few points and then drawing a straight line through them. The points that are on or below the line satisfy the inequality.
(c) x - 2y ≥ -10
This inequality represents a line with the equation x - 2y = -10. You can graph this line by plotting a few points and then drawing a straight line through them. The points that are on or above the line satisfy the inequality.
(d) y ≤ -2x + 10
This inequality represents a line with the equation y = -2x + 10. You can graph this line by plotting a few points and then drawing a straight line through them. The points that are on or below the line satisfy the inequality.
The set of points that satisfy all three inequalities is the area that is not shaded in the graph.
(ii) To find the maximum number of rabbits the farmer can buy, we need to find the coordinates of the vertex of the feasible region.
The coordinates of the vertex of the feasible region is (x,y) the point where the line 2x+3y=30 and x-2y=-10 intersects.
We can substitute the x-2y=-10 into the 2x+3y=30 equation
2x+3y=30
2x+3y+2y=-10
2x+5y=-10
x=-5y+10
substituting this into one of the equation we have
2(-5y+10)+3y=30
-10y+20+3y=30
-7y=10
y= -10/7
substituting this into x = -5y+10 we have
x = -5(-10/7)+10 = 15
the maximum number of rabbits the farmer can buy is 15
Explanation: