Question

3. (10 points) Whole Grains is a small bakery that supplies four major customers with bread ea morning. If we locate the bakery at the origin of a grid [i.c., at the point (0,0)], then the four customer locations and their daily requirements are Daily Requirements loaves) Customer Location (15, 30) (5, 30) (10, 20) (5, 5) 8s 162 26 140 The bakery has several delivery trucks, each having a capacity of 250 loaves. Assume the cost traveling between any two locations is simply the straight-line or Euclidean distance between any two points shown below 33.5 304 22.4 7.1 10 11.2 26.9 25 15.8 11.2 Show the delivery routels) the bakery should take to meet customers' daily requirements.

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Answer 1

Cost Savings for each pair of customer locations:

Let saving be denoted by ‘s’ and cost by ‘c’.

s₁₂ = c₀₁ + c₀₂ – c₁₂ = 33.5 + 30.4 – 10 = 53.9

s₁₃ = c₀₁ + c₀₃ – c₁₃ = 33.5 + 22.4 – 11.2 = 44.7

s₁₄ = c₀₁ + c₀₄ – c₁₄ = 33.5 + 7.1 – 26.9 = 13.7

s₂₃ = c₀₂ + c₀₃ – c₂₃ = 30.4 + 22.4 – 11.2 = 41.6

s₂₄ = c₀₂ + c₀₄ – c₂₄ = 30.4 + 7.1 – 25 = 12.5

s₃₄ = c₀₃ + c₀₄ – c₃₄ = 22.4 + 7.1 – 15.8 = 13.7

Customer Pair Ranking in diminishing order of saving amounts:

Rank = (1,2), (1,3), (2,3), (1,4), (3,4), (2,4).

For pair (1,2), load = 85 + 162 = 247 (less than truck load of 250).

So one route will cover customer locations 1 and 2 from the bakery.

No other customer location can be covered in that route as it will exceed truck capacity.

For pair (3,4), load = 26 + 140 = 166 (less than truck load of 250).

So second route will cover customer locations 3 and 4 from the bakery.

No other customer location can be covered in that route as it will exceed truck capacity.

The delivery routes are shown below:

30 20 15 lo Bakeryxp-t--ㄒㄧㄒㄧㄒㄒ少 lo 15 20 25 15 20 2 ku=Cust omer ocation. Delivery Routes