-------------------------------------------- Linear Program----------------------------------------------------

_{Decision Variables:}

x_ij: # of units to ship from WH i to Customer j

_{Objective Function:}

min. z= 25x₁₁+21x₁₂+11x₁₃+21x₁₄+23x₂₁+16x₂₂+17x₂₃+21x₂₄+

20x₃₁+20x₃₂+14x₃₃+25x₃₄+17x₄₁+25x₄₂+16x₄₃+12x₄₄

_Constraints:

x₁₁+x₁₂+x₁₃+x₁₄ 2,500

x₂₁+x₂₂+x₂₃+x₂₄ 2,500

x₃₁+x₃₂+x₃₃+x₃₄ 2,500

x₄₁+x₄₂+x₄₃+x₄₄ 2,500

x₁₁+ x₂₁+ x₃₁+ x₄₁=1,200

x₁₂+ x₂₂+ x₃₂+ x₄₂=800

x₁₃+ x₂₃+ x₃₃+ x₄₃=5,250

x₁₄+ x₂₄+ x₃₄+ x₄₄=1,850

X_ij 0, integer

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Question 13: (Based on the Linear Program provided for Question 12 above)

After you have developed the transportation schedule, you receive a note with more considerations to add to the linear program. The considerations are provided in the list below.

How would you add them to the Linear Program? Write the necessary part(s).

1. Customer 2 should be serviced completely by Warehouse 1.
2. The amount shipped to Customer 3 by Warehouse 2 should be at least as much as the amount shipped to Customer 3 by Warehouse 4.
3. Customer 3 has reached out and let you know that the demand they have was reported in error, and that they would be okay with receiving less than their demand, however the minimum amount they should receive is 2,000. i) Which constraint from the original Linear Program should be edited to accommodate this change? ii) What should be the new constraint(s)?