1. **State the problem:** We need to transport 1200 bags using two types of vehicles: Pickup trucks and Isuzu Diana trucks. 2. **Define variables:** Let $x$ be the number of trips made by Pickup trucks and $y$ be the number of trips made by Isuzu Diana trucks. 3. **Write down the constraints:** - Each Pickup trip carries 18 bags, so total bags by Pickup = $18x$. - Each Isuzu Diana trip carries 30 bags, so total bags by Isuzu Diana = $30y$. - Total bags transported must be 1200: $$18x + 30y = 1200$$ - The number of Pickup trips should not exceed Isuzu Diana trips by more than 2: $$x - y \leq 2$$ - Cost per Pickup trip is 240,000 and per Isuzu Diana trip is 300,000. - Total budget is 2,400,000: $$240000x + 300000y \leq 2400000$$ 4. **Simplify the equations:** - Divide the bag equation by 6: $$\frac{18x}{6} + \frac{30y}{6} = \frac{1200}{6} \Rightarrow 3x + 5y = 200$$ - Divide the budget inequality by 60,000: $$\frac{240000x}{60000} + \frac{300000y}{60000} \leq \frac{2400000}{60000} \Rightarrow 4x + 5y \leq 40$$ 5. **Express $x$ from the bag equation:** $$3x + 5y = 200 \Rightarrow 3x = 200 - 5y \Rightarrow x = \frac{200 - 5y}{3}$$ 6. **Apply the trip difference constraint:** $$x - y \leq 2 \Rightarrow x \leq y + 2$$ 7. **Substitute $x$ into the budget inequality:** $$4x + 5y \leq 40$$ Substitute $x$: $$4\left(\frac{200 - 5y}{3}\right) + 5y \leq 40$$ Multiply both sides by 3 to clear denominator: $$4(200 - 5y) + 15y \leq 120$$ $$800 - 20y + 15y \leq 120$$ $$800 - 5y \leq 120$$ $$-5y \leq 120 - 800$$ $$-5y \leq -680$$ Divide both sides by -5 (reverse inequality): $$y \geq 136$$ 8. **Check integer solutions:** - Since $y \geq 136$, try $y=136$: $$x = \frac{200 - 5(136)}{3} = \frac{200 - 680}{3} = \frac{-480}{3} = -160$$ (not possible, negative trips) - Try $y=40$ (from budget inequality): $y$ must be at least 136, so no solution under budget. 9. **Conclusion:** The budget constraint is too low to transport 1200 bags with the given trip capacities and costs. **Final answer:** No feasible solution exists under the given constraints.