Engineering Optimization: Theory and Practice, Fourth Edition

Problems 163 3.10 Find the solution of the following problem by the graphical method: Minimizef=x 12 x 22 subject to x 13 x 22 ≥ ...

164 Linear Programming I: Simplex Method −x+ 6 y≥ 12 5 x+ 2 y≤ 68 x≤ 10 x≥ 0 , y≥ 0 3.17 Rework Problem 3.16 by changing the obj ...

Problems 165 3.23 Maximizef=x+ 3 y subject to − 4 x+ 3 y≤ 12 x+y≤ 7 x− 4 y≥ 2 x≥ 0 , y≥ 0 3.24 Minimizef=x−^8 y subject to 3 x+ ...

166 Linear Programming I: Simplex Method 9 x+ 7 y≤ 108 3 x+ 7 y≤ 70 2 x− 5 y≥ − 35 x≥ 0 , y≥ 0 3.28 Minimizef=x− 4 y subject to ...

Problems 167 subject to 10 x+y≥ 10 5 x+ 4 y≥ 20 3 x+ 7 y≥ 21 x+ 12 y≥ 12 x≥ 0 , y≥ 0 3.33 Rework Problem 3.32 by changing the ob ...

168 Linear Programming I: Simplex Method subject to 3 x+ 4 y≤ 24 x−y≤ 3 x+ 4 y≤ 4 3 x+y≥ 3 x≥ 0 , y≥ 0 3.40 Maximizef=^3 x+^2 y ...

Problems 169 3.44 Reduce the system of equations 2 x 1 + 3 x 2 − 2 x 3 − 7 x 4 = 2 x 1 +x 2 −x 3 + 3 x 4 = 12 x 1 −x 2 +x 3 + 5 ...

170 Linear Programming I: Simplex Method limit on the lengths of the standard rolls, find the cutting pattern that minimizes the ...

Problems 171 Solve Problems 3.54–3.90 by the simplex method. 3.54 Problem 1.22 3.55 Problem 1.23 3.56 Problem 1.24 3.57 Problem ...

172 Linear Programming I: Simplex Method 3.85 Problem 3.38 3.86 Problem 3.39 3.87 Problem 3.40 3.88 Problem 3.41 3.89 Problem 3. ...

Problems 173 The times available on machinesA 1 andA 2 per day are 1200 and 1000 minutes, respec- tively. The profits per unit o ...

174 Linear Programming I: Simplex Method 3.97 A bank offers four different types of certificates of deposits (CDs) as indicated ...

Problems 175 Quantity of coal required to generate 1 Pollution Cost of coal MWh at the power caused at at power plant (tons) pow ...

176 Linear Programming I: Simplex Method Assuming that a particular process can be employed for any number of days in a 30-day m ...

4 Linear Programming II: Additional Topics and Extensions 4.1 Introduction If a LP problem involving several variables and const ...

178 Linear Programming II: Additional Topics and Extensions 1.The relative cost coefficientscjto compute† cs= inm (cj) (4.1) csd ...

4.2 Revised Simplex Method 179 subject to AX=A 1 x 1 +A 2 x 2 + · · · +Anxn=b (4.4) X n× 1 ≥ 0 n× 1 (4.5) where thejth column of ...

180 Linear Programming II: Additional Topics and Extensions Definition. The row vector cTBB−^1 =πT=      π 1 π 2 .. . π ...

4.2 Revised Simplex Method 181 and the modified cost coefficientcjas cj=cj−πTAj (4.10) Equations (4.9) and (4.10) can be used to ...

182 Linear Programming II: Additional Topics and Extensions only to illustrate the transformation, and it can be dropped in actu ...