Manufacturer has two factories, located in Toronto and Winnipeg. Warehouses are located in Moncton, Montreal, and Calgary. Minimum requirements at the three warehouses are for at least $5000,8000,$ and $7000$ units, respectively. The production capacities of the two factories are $9000$ and $13000$ units, respectively. Shipping costs per unit from each factory to each warehouse are given below:

WAREHOUSE

Required

The manufacturer wants to determine the optimal shipping schedule that will minimize transportation costs.

Required

i$.$ Formulate the linear programming model for this problem. $[4$ Marks$]$

ii$.$ Generate initial solution using Vogel's Approximation Method and the Least Cost Method $[6$ Marks$]$

iii. Test the solution for optimality generated using the stepping stone Method $[10$ Marks$]$