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barxatty [35]
3 years ago
11

Suppose that one wishes to schedule vehicles from a central depot to five customer locations. The distance of making trips betwe

en each pair of locations is given in the following matrix. (The trip distances are symmetrical and the depot is location 0 below). 0 1 2 3 4 5 0 0 20 75 33 10 30 1 0 35 5 20 15 2 0 18 58 42 3 0 40 20 4 0 25 5 0 Assume that each vehicle is constrained to travel no more than 50 miles on each route (for example they are electric and need to return to the depot to be recharged at least every 50 miles of travel). Find the routing suggested by the savings method.
Mathematics
1 answer:
sladkih [1.3K]3 years ago
3 0

Answer:

The routing suggested by the savings method is route (3,4)

Step-by-step explanation:

Savings for all trips (i, j), 1 ≤ i ∠ j ≤ 5

Total  number of trips to be commuted = 10 trips

S₁₂ = C₀₁ + C₀₂ - C₁₂ = 20 + 75 - 35 = 60

S₁₃ = C₀₁ + C₀₃ - C₁₃ = 20 + 33 - 5 = 48

S₁₄ = C₀₁ + C₀₄ - C₁₄ = 20 + 10 - 20 = 10

S₁₅ = C₀₁ + C₀₅ - C₁₅ = 20 + 30 - 15 = 35

S₂₃ = C₀₂ + C₀₃ - C₂₃ = 75 + 33 - 18 = 90

S₂₄ = C₀₂ + C₀₄ - C₂₄ = 75 + 10 - 58 = 27

S₂₅ = C₀₂ + C₀₅ - C₂₅ = 75 + 30 - 42 = 63

S₃₄ = C₀₃ + C₀₄ - C₃₄ = 33 + 10 - 40 = 3

S₃₅ = C₀₃ + C₀₅ - C₃₅ = 33 + 30 - 20 = 43

S₄₅= C₀₄ + C₀₅ - C₄₅ = 10 + 30 - 25 = 15

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On a quiz show, Linda won $10 less than three times as much as Charlie. If Linda won $800, how much did Charlie win?
PilotLPTM [1.2K]

Using a system of equations, it is found that Charlie won $270.

<h3>What is a system of equations?</h3>

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are:

  • Variable x: Amount earned by Linda.
  • Variable y: Amount earned by Charlie.

Linda won $10 less than three times as much as Charlie, hence:

x = 3y - 10

Linda won $800, hence the amount won by Charlie is found as follows:

800 = 3y - 10

3y = 810

y = 810/3

y = 270

More can be learned about a system of equations at brainly.com/question/24342899

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Number 2 uses the same process, but changing to using C instead of A

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