What is the minimum expense? A new route is now available, going from the top sh

Question

What is the minimum expense?

A new route is now available, going from the top shipping terminal, to the top customer on the graph. The expense to use this route is $2.50 per unit.
How many will be shipped down the new route?

What is the new minimum expense?

In addition to the new route mentioned above, the shipping route between the bottom factory and the bottom customer is now available at a reduced price: $7.50

how many will be shipped along this route now?

What is the new minimum expense? with both of the above changes?

Factories customers Needs 2000 $23/unit 1200 max $2 Shipping terminals $2 $3 $3> 900 ma $29/unit 2900 ma 900 max Needs1100 $2 $2 S4,9 $5 $4 2800 max S3.5 $2 Needs2100 $19/unit 1900 max $11.50

Explanation / Answer

There are Three Factories, say F1, F2, and F3; two transhipments (intermediate) say W1 and W2; three destinations of customers say D1, D2, and D3. Decision variables, objective function and constraints are represented with the help of following matrix.

Solution using Excel sover is as follows:

Minimum expense calculated as above is $167,500

Additional route is from W1 to D1 @ $2.5 so new variable W1D1 may be introduced

Cost of Transportation per unit FromTo W1 W2 D1 D2 D3 Maximum F1 25 31.5 1200 F2 32 31 2900 F3 21 30.5 1900 W1 2 1900 W2 4.5 3.5 2800 D1 3 D2 1 5 D3 4 Demand 1900 2800 2000 1100 2100

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