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Zorluk: OrtaSystems of Linear Inequalities in Two Variables

A logistics company uses a delivery drone to transport two types of packages. Let xx represent the number of Type A packages and yy represent the number of Type B packages in a single flight. The drone can carry at most 12 packages in total. Additionally, to balance the drone, the total weight of the cargo must be at least 15 pounds. Each Type A package weighs 2 pounds, and each Type B package weighs 1 pound. Which of the following combinations of Type A and Type B packages is a viable shipment for the drone?

  1. A
    3 Type A packages and 8 Type B packages
  2. B
    4 Type A packages and 5 Type B packages
  3. 5 Type A packages and 6 Type B packagesCevap
  4. D
    6 Type A packages and 7 Type B packages

Cevap

5 Type A packages and 6 Type B packages
The correct combination of 5 Type A packages and 6 Type B packages satisfies all system requirements. The total package count of 11 is less than or equal to the drone's limit of 12 packages (5+6≤125 + 6 \leq 12). Furthermore, the total weight of 16 pounds meets the minimum balance requirement of 15 pounds (2(5)+6≥152(5) + 6 \geq 15).

Adım Adım Çözüm

1
Write the system of linear inequalities that represents the given constraints.
The capacity constraint is x+y≤12x + y \leq 12, and the weight constraint is 2x+y≥152x + y \geq 15, where xx and yy are non-negative integers.
To define the mathematical boundaries for a valid shipment.
2
Substitute the package counts from the correct combination into both inequalities to verify they are satisfied.
For 5 Type A packages (x=5x = 5) and 6 Type B packages (y=6y = 6):
- Package count: 5+6=11≤125 + 6 = 11 \leq 12 (True)
- Cargo weight: 2(5)+6=16≥152(5) + 6 = 16 \geq 15 (True)
To confirm that the chosen combination satisfies all system requirements.

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Systems of Linear Inequalities in Two Variables
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Systems of Linear Inequalities in Two Variables

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