Question

There are three factories producing bath tubs have capacities as follows - Des Monies 100 tubs per day - Evansville 300 tubs per day - Fort Lauderdale 300 tubs per day These tubs need to be shipped to three warehouses whose demands are as follows - Albuquerque 300 tubs per day - Boston 200 tubs per day - Cleveland 200 tubs per day. Cost of shipping one tub from each factory to each warehouse are as follows Des Monies to Albuquerque $5, Evansville to Albuquerque $8, Fort Lauderdale to Albuquerque $9 Des Monies to Boston $4, Evansville to Boston $4, Fort Lauderdale to Boston $7 Des Monies to Cleveland $3, Evansville to Cleveland $3, Fort Lauderdale to Cleveland $5 The problem is to determine how much each factory needs to ship to each warehouse so that the demands are met within the capacity limits and the total costs are minimum Write the LP formulation for the above problem

Answer 1

Please refer to the solution below.

2 FRIDAY September 2016 WEEK 36 Factory Pan (tubs/day) Des Monies 100 Evansville 300 Fort Lauderdale 300 Warchouse Albuquerque Boston cleveland Demand (tubs/day) 300 200 200 Cost of Shipping ($1 tub) Albuquerque Boston Cleveland Des Monies 5 니 3 Evansville 8 4 3 Fort Lauderdale 9 7 5 Let xij LP - No of tubs sent berday from factory i to warehouse j il Des Monics j = 1 Albuquerque 2- Evansville 2- Boston 3 Fort Lauderdale 3₃ cleveland Objective function: To minimize total cost of shipping DS GROUP SS