Question

1. The transportation problem done in class is to find how many generators should be shipped from each manufacturing facility to each distribution center so that shipping cost is minimized. To remind you, the LP is Min Transportation costs: 3x11 + 2 x12 + 7 x13 + 6 x14 + 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: ◦ xij ≥ 0 for i = 1 to 3, j = 1 to 4 Changing the production capacity of York to 3,500 generators, because they just upgraded their equipment. 1) Then 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) 2) Then give the minimum transportation cost. 3) Is there any slack or surplus? Is the slack in York or somewhere else? 4) What are the binding constraints?

Answer 1