Question

Dana Johnson Corp. is considering adding a fourth plant to its three existing facilities in Decatur, Minneapolis, and Carbondale. Both St. Louis and East St. Louis are being considered. Evaluating only the transportation costs per unit as shown in the table, decide which site is best. From Existing Plants Minneapolis To Blue Earth Ciro Des Moines Capacity Decatur $20 $25 $22 450 $17 $27 $25 350 Carbondale $21 $20 $22 150 Demand 450 250 500 From Proposed Plants To Blue Earth Ciro Des Moines Capacity East St. Louis $29 $30 $30 250 St. Louis $27 $28 $31 250 V, with a total cost of $(enter your Comparing the total cost at two locations, Dana Johnson Corp. should select response as a whole number) East St. Louis St. Louis

Answer 1

>> When East St. Louis is selected,

Carbondale East St.Louis Demand Minneapolis Tol From Blue Earth Ciro Des Moines Capacity 450 250 500 21 29 17 27 25 350 20 25 150 250 Decision Variables Number of units to be transported from each plant to each location Carbondale East St.Louis Minneapolis Tol From Blue Earth Ciro Des Moines 10 Objective function 12 13 14SUMPRODUCT(B9:E11,B2:E4 15 16SUM B9:E9) 7 SUM(810:E10) 18 SUM(B11:E11) 19 -SUM(B9:B11) 20 -SUM(C9:C11) 21 -SUM(D9:D11) 22 SUM(E9:E11 Minimize the total costs Constraints -F2 -F3 -B5

To From Blue Earth Ciro Des Moines Capacit DecaturMinneapolis Carbondale East St.Louis Demand 20 17 21 30 30 250 20 250 500 450 350 Decision Variables Number of units to be transported from each plant to each location To From Blue Earth Ciro Des Moines DecaturMinneapolis Carbondale East St.Louis Objective function 12 13 Minimize the total costs Constraints 16 | 17 18 19 20 21 250

Decision Variables Number of units to be transported from each plant to each location To From Blue Earth Ciro Des Moines Decatur Minneapolis Carbondale East St.Louis 100 0 350 350 0 0 0 0 100 0 12 Objective function Minimize the total costs 4 5 l6 26150 Constraints 350 350

>> When St. Louis is selected,

To From Blue Earth Ciro Des Moines Capacity DecaturMinneapolis Carbondale St.Louis Demand 17 27 21 27 28 31 250 20 450 250 500 20 450 350 Decision Variables Number of units to be transported from each plant to each location DecaturMinneapolis Carbondale St.Louis To From Blue Earth Ciro Des Moines 10 Objective function Minimize the total costs Constraints 17 18 19 21

Solver Parameters SAS14 Set Objective To: Ma Min By Changing aiable Cells: Value Of: SBS9:SES11 na 50 50 Subject to the Constraints: SAS16: SAS22 = SCS 16:SCS22 SBS9:SESI 1 >= 0 Add Change Delete Reset All Load/Save Make Unconstrained Variables Non-Negative Select a SolvingSimplex LP Method: 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 Solve Close

Decision Variables Number of units to be transported from each plant to each location Decatur Minneapolis Carbondale St.Louis To From Blue Earth Ciro Des Moines 350 0 0 100 150 0 0 0 10 0 100 Objective function 12 13 Minimize the total costs 25850 Constraints 16 17 18 19 20 350 150 350

St. Louis gives lesser costs

St. Louis must be selected with a total cost of $25,850