Bruce's Material Company hauls gravel to a construction site, using a small truck and a large truck. The carrying capacity and operating cost per load are given in the accompanying table. Bruce must deliver a minimum of 300 cubic yards per day to satisfy his contract with the builder. The union contract with his drivers requires that the total number of loads per day is a minimum of 7.**How many loads should be made in each truck per day to minimize the total cost?**| | Small Truck | Large Truck ||------------------|-------------|-------------|| Capacity (yd³) | 50 | 60 || Cost per Load | $72 | $54 |In order to minimize the total cost, the number of loads in a small truck that should be made is [blank], and the number of loads in a large truck that should be made is [blank].

Answered: Bruce's Material Company hauls gravel…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Bruce's Material Company hauls gravel to a construction site, using a small truck and a large truck. The carrying capacity and operating cost per load are given in the accompanying table. Bruce must deliver a minimum of 300 cubic yards per day to satisfy his contract with the builder. The union contract with his drivers requires that the total number of loads per day is a minimum of 7.

**How many loads should be made in each truck per day to minimize the total cost?**

| | Small Truck | Large Truck |
|------------------|-------------|-------------|
| Capacity (yd³) | 50 | 60 |
| Cost per Load | $72 | $54 |

In order to minimize the total cost, the number of loads in a small truck that should be made is [blank], and the number of loads in a large truck that should be made is [blank].

Expert Solution

Step 1

This is a Linear Programming Problem, which we shall solve by the graphical method.

1. Define the variables:
Let X represent the Small Truck, Y represent the Large Truck.
Let Z: define the total cost function.

2. The objective is to determine the number of loads per day, such that the value of Z is minimized.
Minimize Z: 72 X + 54 Y

3. Mention the constraints:
It is given that Bruce must deliver at least 300 cubic yards per day.
$\Rightarrow 50 X + 60 Y \geq 300$

Next, the contract requires that the total number of loads per day is minimum 7.
$\Rightarrow X + Y \geq 7$