This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
You're on a roll — a) Step 1: Define variables. Let x be the number of trips made by the FTR lorry. Let y be the number of trips made by the canter lorry. Step 2: Formulate inequalities based on the problem statement. • "The canter has to make at most twice as many trips as the FTR makes." y 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 1000 This simplifies to: 4x + y 50 • "The canter has to make more than 10 trips." y > 10 • Implicitly, the number of trips cannot be negative. Since y > 10, y 0 is already satisfied. We also need: x 0 Step 3: List all the possible inequalities. The inequalities are: 1. y 2x 2. x + y < 30 3. 4x + y 50 4. y > 10 5. x 0 b) To represent the information on a grid: Step 1: Draw and label the axes. Draw a horizontal x-axis (for FTR trips) and a vertical y-axis (for canter trips). Since x 0 and y > 10, focus on the first quadrant, with the y-axis starting above 10. Step 2: Draw the boundary lines for each inequality. • For y 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 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 0, this is the y-axis. This line should be solid. Step 3: Shade the feasible region. Determine the region that satisfies each inequality: • For y 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 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 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. Got more? Send 'em 📸