Question

Using the LP Formulation below and excel solver, explain step by step how to turn it into a linear programming model.

Decision Variables: Let
xij= units to be shipped from supplier I to customer j, where
i= 1- supplier 1 = 2- supplier 2 = 3- supplier 3 = 4- Toledo supplier
j= A- customer a = B- customer b = C- customer c

Objective Function: The objective is to minimize transportation costs with Toledo supplier.
          10x1a+14x1b+10x1c+12x2a+17x2b+20x2c+11x3a+11x3b+12x3c+18x4a+8x4b+14x4c

Constraints:
Supplier 1 available: x1a+x1b+x1c <= 200
Supplier 2 available: x2a+x2b+x2c <= 140
Supplier 3 available: x3a+x3b+x3c <= 150
Toledo Supplier available: x4a+x4b+x4c <= 200

Customer A demand: x1a+x2a+x3a+x4a >= 220
Customer B demand: x1b+x2b+x3b+x4b >= 220
Customer C demand: x1c+x2c+x3c+x4c >= 220

Answer 1

From To Supplier 1 Supplier2 Supplier 3 Toldeo 10 12 14 17 10 20 12 14 4 18 Decision Variables Number of units to be shipped from each supplier to customer From To Supplier 1 Supplier2 Supplier 3 Toldeo 10 12 Obiective function 14 SUMPRODUCT(B9:D12,B2:D5) Minimize costs Constraints 16 SUM(B9:D9) 17 SUM(B10:D10) 18 SUM(B11:D11) 19 -SUM(B12:D12) 20 SUM(B9:B12) 21 |:SUM(C9:C12) 22 SUM(D9:D12) 200 140 200 220 220 220