Correct answer is (This constraint describes capacity constraint of plan B)

B. | *x*2*P* + *x*2*A* + *x*2*D* + *x*2*L* ≤ 400 |

Let,In this case, Decision variables have been identified as,

xij = number of units shipped from plant i to regional center j where i = {1,2,3,A=4} and j = {Philadelphia = P,Atlanta=A,Dallas=D,Los Angeles=L}

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For your reference please find the solution below

With Plant A,

Let,

xij = number of units shipped from plant i to regional center j where i = {1,2,3,A=4} and j = {Philadelphia = 1,Atlanta=2,Dallas=3,Los Angeles=4}

Spreadsheet model

Formula used

Solver window input

Solving in solver we get following optimal schedule

| Philadelphia | Atlanta | Dallas | Capacity |

Plant 1 | 100 | 300 | 0 | 0 |

Plant 2 | 0 | 0 | 0 | 350 |

Plant 3 | 250 | 0 | 0 | 0 |

Plant A | 0 | 50 | 350 | 0 |

Minimized cost = 148350

With Plant B,

Spreadsheet model

Formula used

Solver window input

Solving in solver we get following optimal schedule

| PhilaDelphia | Atlanta | Dallas | Capacity |

Plant 1 | 50 | 350 | 0 | 0 |

Plant 2 | 0 | 0 | 0 | 350 |

Plant 3 | 300 | 0 | 0 | 0 |

Plant B | 0 | 0 | 350 | 0 |

Minimized cost = 148550

A B C D E F G H I J K L M N O P Q R S T U v Objective function 148350 0 24x31x32x33x34x41x42x43x44 350 250 0 0 0 0 50 350 0 x11 x12x13x14x21 22 23 100 300 0 0 0 0 1 1 1 1 1 1 400 <= 350 1 250 1 3 4 Plant 1 5 Plant 2 6 Plant 3 7 Plant A 8 Philadelphia 9 Atlanta 10 Dallas 11 Capacity 12 400 400 400 400 350 350 350 350 1 350 = 350 = 350 = 1 350 =

4 A B C D E F G H I J K L M N O P Q R S T U Objectiv x11 x12 x13x14x21 x22x23x24 x31 x32 33 34 x41 42 43 44 function=896B3+75*C393 D3+115 E3+120*F3+88*G3+103*H3+93*13+9513+82 K3+112 L3+98*M3+94*N3+780395*P3+95 Q3+23500 100 300 0 0 0 0 0 350 250 0 0 0 0 50 350 0 4 Plant 1 1 1 1 1 =SUMPRODUCT($B$3:5Q$3,B4:04) <= 400 5 Plant 2 1 1 1 1 =SUMPRODUCT($B$3:5Q$3,85:05) <= 400 6 Plant 3 1 1 1 1 =SUMPRODUCT($B$3:5Q$3,06:06) <= 400 7 Plant A 1 1 1 1 =SUMPRODUCT($B$3:$Q$3,17:07) <= 400 PhilaD 8 elphia 1 =SUMPRODUCT($B$3:5Q$3,38:08) = 350 9 Atlanta =SUMPRODUCT($B$3:5Q$3,19:09) = 350 10 Dallas =SUMPRODUCT($B$3:5Q$3,B10:010 = 350 11 Capacity 1 =SUMPRODUCT($B$3:5Q$3,B11:01: = 350 12

Solver Parameters Set Objective: sv52 Value Of: To: O Max O Min By Changing Variable Cells: $B$3:5053 Subject to the Constraints: SR$4:$R$7 <= $T$4:$T$7 SR$8:SRS11 = $T$8:$T$11 Add Change Delete Reset All Load/Save ✓ Make Unconstrained variables Non-Negative Select a Solving Method: Simplex LP Options Solving Method Select the GRG Nonlinear engine for Solver Problems that are smooth nonlinear. Select the LP Simplex engine for linear Solver Problems, and select the Evolutionary engine for Solver problems that are non-smooth. Help I solve [ close

B C D E F G H I J K L M N O P Q R S Objective function 148550 x11x12x13x14x21x22 50 350 0 0 0 1 1 1 1 x23x24 x31x32 0 0 350 300 233 0 234 0 241 x42x43x44 0 0 0 350 1 0 1 4 Plant 1 5 Plant 2 6 Plant 3 7 Plant B 400 <= 350 <= 300 <= 350 <= 1 400 350 8 Philadelphia 9 Atlanta 10 Dallas 11 Capacity 350 = 350 = 350 = 350 = 350 350

A B C D E F G H I J K L M N O P Q T U Objectiv function = 89'B3+75 C3+93 D3+115'E3+120"F3+88"G3+103'H3+93'13+95 J3+82 K3+112'L3+98 M3+95 N3+88'O3+88*P3+94'Q3+26000 4 5 6 7 211 212 213 214 221 222 223 224 231 50 350 0 0 0 0 0 350 300 Plant 1 1 1 1 1 Plant 2 1 1 1 1 Plant 3 1 Plant B PhilaDelphi 232 233 234 x41x42 243 244 0 0 0 0 0 350 0 =SUMPRODUCT($B$3:$Q$3,B4:04) =SUMPRODUCT($B$3:$Q$3,B5:05) 1 1 1 =SUMPRODUCT($B$3: $Q$3,B6:06) = SUMPRODUCT($B$3:$0$3,B7:07) <= 400 <= 400 <= 400 <= 400 9 10 11 Atlanta Dallas Capacity = SUMPRODUCT($B$3:$0$3,38:08) = 350 =SUMPRODUCT($B$3:$Q$3,69:Q9) = 350 =SUMPRODUCT($B$3:$Q$3,B10:Q10) = 350 =SUMPRODUCT($B$3:$Q$3,B11:Q11) = 350

Solver Parameters Set Objective: sv52 Value Of: To: O Max O Min By Changing Variable Cells: $B$3:5053 Subject to the Constraints: SR$4:$R$7 <= $T$4:$T$7 SR$8:SRS11 = $T$8:$T$11 Add Change Delete Reset All Load/Save ✓ Make Unconstrained variables Non-Negative Select a Solving Method: Simplex LP Options Solving Method Select the GRG Nonlinear engine for Solver Problems that are smooth nonlinear. Select the LP Simplex engine for linear Solver Problems, and select the Evolutionary engine for Solver problems that are non-smooth. Help I solve [ close

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