Question

To remind you, the LP is

Min Transportation costs: 3x₁₁ + 2 x₁₂ + 7 x₁₃ + 6 x_{14 +} 7x₂₁ + 5 x₂₂ + 2 x₂₃ + 3 x₂₄ + 2x₃₁ + 5 x₃₂ + 4 x₃₃ + 5 x₃₄

s.t.

Need to make sure demand at destination is satisfied:

• Boston demand: x₁₁ + x₂₁ + x₃₁ = 6000
• Chicago demand: x₁₂ + x₂₂ + x₃₂ = 4000
• St. Louis demand: x₁₃ + x₂₃ + x₃₃ = 2000
• Lexington demand: x₁₄ + x₂₄ + x₃₄ = 1500

Amount shipped can’t equal more than plant can make:

• Cleveland: x11 + x12 + x13 + x14 ≤ 5000
• Bedford: x21 + x22 + x23 + x24 ≤ 6000
• York: x31 + x32 + x33 + x34 ≤ 2500
• Note: all these constraints have units of ‘generators’

Non-negativity:

• x_ij ≥ 0 for i = 1 to 3, j = 1 to 4

1. Rerun the above problem, but changing the production capacity of York to 3,500 generators, because they just upgraded their equipment.

NOTE THIS IS NOT THE SAME CHANGE DONE IN CLASS, MAKE SURE YOU CHANGE YOUR CONSTRAINTS ACCORDINGLY.

1. Redraw the transportation diagram with the new constraint. (put this image into the excel sheet).
2. Do you need a dummy node here? Why or why not?
3. Give the DVs, objective function and constraints.
4. Solve the problem in solver
5. Give a short writeup stating how many generators are shipped from each plant to each distribution center (in other words, give the values for the Xij, but use words rather than variables so your boss knows what you are talking about. A table similar to the shipping cost table would be good, for example) . Again, you are trying to summarize the results for your busy boss.
6. Then give the minimum transportation cost.
7. Is there any slack or surplus?
8. What are the binding constraints?
9. Compare your results here with what you saw in the sensitivity analysis report of the RHS for problem 1.
   1. Is the change for York within the allowable increase given in Problem 1?
   2. If so, if you used the shadow price for York in problem, does that added to the original shipping cost equal the shipping cost you got here in Problem 2?

Answer 1