COT 6401The Analysis of AlgorithmsTest (March 11, 2009)Due:midnight of March 12, 2009Name —————————————- SSN —————————————-1. (20%) (Greedy) A telecom company needs to install base stations to cover all houses alonga long road. These houses can be sparsely distributed along the road. Suppose the coverageof each base station is 5 miles. Design anoptimal solutionthat covers all houses using as fewbase stations as possible. Prove that your algorithm is optimal.2. (20%) (Linear programming) Solve the following linear program using SIMPLEX and showall the relevant steps:maximizex1+ 2x2subject to4x1-x2≤9x1+x2≤85x1-2x2≥ -3x1, x2≥0Provide a geometric explanation of the solution by plotting the correspondingfeasible regionin a 2-D space.3. (20%) (Divide-and-conquer) Suppose the only way to access a database of student GPA isthrough a simple querykand that the system returns thekthsmallest value that it contains.
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