A transporter wishes to transfer 1000 bags of sugar. An FTR lorry can carry 80 bags and a canter lorry can carry 20 bags. The canter has to make at most twice as many trips as the FTR, and the total n

Let $x$ be the number of trips made by the FTR lorry.
Let $y$ be the number of trips made by the canter lorry.

• "The canter has to make at most twice as many trips as the FTR makes." $$y \le 2x$$
• "The total number of trips made by both lorries must be less than 30." $$x + y < 30$$
• "A transporter wishes to transfer 1000 bags of sugar." FTR capacity is 80 bags, canter capacity is 20 bags. The total bags transferred must be at least 1000. $$80x + 20y \ge 1000$$ This simplifies to: $$4x + y \ge 50$$
• "The canter has to make more than 10 trips." $$y > 10$$
• Implicitly, the number of trips cannot be negative. Since $y > 10$, $y \ge 0$ is already satisfied. We also need: $$x \ge 0$$

The inequalities are:

1. $y \le 2x$
2. $x + y < 30$
3. $4x + y \ge 50$
4. $y > 10$
5. $x \ge 0$

Draw a horizontal x-axis (for FTR trips) and a vertical y-axis (for canter trips). Since $x \ge 0$ and $y > 10$, focus on the first quadrant, with the y-axis starting above 10.

• For $y \le 2x$, draw the line $y = 2x$. This line should be solid.
• For $x + y < 30$, draw the line $x + y = 30$. This line should be dashed.
• For $4x + y \ge 50$, draw the line $4x + y = 50$. This line should be solid.
• For $y > 10$, draw the line $y = 10$. This line should be dashed.
• For $x \ge 0$, this is the y-axis. This line should be solid.

Determine the region that satisfies each inequality:

• For $y \le 2x$, shade the region below or on the line $y = 2x$.
• For $x + y < 30$, shade the region below the line $x + y = 30$.
• For $4x + y \ge 50$, shade the region above or on the line $4x + y = 50$.
• For $y > 10$, shade the region above the line $y = 10$.
• For $x \ge 0$, shade the region to the right or on the line $x = 0$.

The feasible region is the area where all shaded regions overlap. This region represents all possible combinations of trips $(x,y)$ that satisfy all the given conditions.