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Math 308 Hw 4

Linear Optimization (MATH 308) Assignment (Hw) #4

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Math 308 Hw 4

1. 1. ASSIGNMENT 4 MATH 308 - LINEAR OPTIMIZATION DUE: 6 FEBRUARY, 12 NOON. ABRAHAM P. PUNNEN Q1: Solve the following problem using simplex method: Maximize 2x1 + x2 − x3 Subject to x1 + 2x2 ≤ x3 + 5 2x1 − x3 ≤ 8 x2 ≥ −3 + x1 xi ≥ 0, i = 1, 2, 3 Q2: Solve the following problem using simplex method: Maximize 2x1 + x2 Subject to x1 + x2 + x3 ≥ 8 2x1 − x2 + 2x3 ≤ 12 x1 ≥ 0, x2 ≥ 0, x3 ≥ 0 Q3: Consider the problem Maximize CX LPP: Subject to AX = b Show that LPP is either infeasible, or unbounded or has a unique optimal solution. Q4: Show that the system −3x1 + 2x2 + 2x3 = 8 −3x1 + 4x2 + x3 = 7 xj ≥ 0 for j = 1, 2, 3 has a feasible solution which satisﬁes 3x1 + 2x2 + x3 ≥ k where k is any large number. Compute a solution to the system satisfying 3x1 + 2x2 + x3 = 10000. Abraham P. Punnen, Department of Mathematics, Simon Fraser University Surrey, Central City, 250-13450 102nd AV, Surrey, British Columbia,V3T 0A3, Canada, Email: apunnen@sfu.ca 1

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• rashmi

Feb. 14, 2009

Linear Optimization (MATH 308) Assignment (Hw) #4

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