Wi amount pounds of item i loaded onto the truck i

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Unformatted text preview: ortion of X3 < 1 each item loaded) X4 < 1 X5 < 1 X6 < 1 31 X ,X ,X ,X ,X ,X >0 Alternative LP Formulation Using Pounds – Not Proportions • Decision variables in the model can be weight (in pounds) of each item shipped, rather than proportion. • Wi = amount (pounds) of item i loaded onto the truck (i = 1, 2, 3, 4, 5, 6) LP formulation Objective: Maximize load value = $22,500/7500 W1+ $24,000/7500 W2 + $8,000/3000 W3 + $9,500/3500 W4 + $11,500/4000 W5 + $9,750/3500 W6 = $3 W1+ $3.2 W2 + $2.67 W3 + $2.71 W4 + $2.88 W5 + $2.79 W6 subject to: W1 + W2+ W3+ W4 + W5 + W6 < 10,000 (Truck capacity) W1 ≤ 7500 (Maximum weight of W2 ≤ 7500 each item loaded) W3 ≤ 3000 W4 ≤ 3500 W5 ≤ 4000 W6 ≤ 3500 32 Optimal Loading The maximum load value is $31,500 is achieved by loading: • Item 1: 2,500 pounds (= 0.33 of 7,500 pounds) • Item 2: 7,500 pounds (all 7,500 pounds) No other items are selected. The truck is fully loaded. (See the spreadsheet model in worksheets “Transportation (A)” and “Transportation (B)” in file “Learning Kit.xls”.) 33 Summary • More exposure in applying linear programming to a variety of disciplines and applications: – Marketing Resea...
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This note was uploaded on 11/04/2012 for the course IS CB2505 taught by Professor Tommylau during the Spring '12 term at City University of Hong Kong.

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