p3_sp2011 - PRELIM 3 ORIE 3310/5310 April 7 2011 Closed...

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PRELIM 3 ORIE 3310/5310 April 7, 2011 Closed book exam. Justify all work. 1. The following classical model is known as the Caterer’s problem . Napkins can be laundered overnight at a cost of $0.025 each, but with one day’s delay at the cheaper rate of $0.015 each. There are presently 175 clean napkins and 175 dirty napkins in stock and we know that for the following three days a conference is planned which will require 300, 325, and 275 napkins, respectively. The city health code forbids retaining dirty napkins overnight. At the end of the upcoming three-day conference, the restaurant will close for one day; thus all remaining dirty napkins can be laundered at the less expensive rate. a. (10) Formulate this model as a transportation problem. b. (10) Solve the problem by inspection . c. (20) Explain why your procedure in (b) is valid. 2. (30) Suppose A = { a ij } is an m × n matrix with real-valued entries, with the sum of the entries in row i given by r i , 1 i m , and the sum of the entries in column j given by c j , 1 j n . We
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