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:WAREHOUSEMonctonMontrealCalgaryTorontoSh$\mathrm{.}20$Sh$\mathrm{.}16$Sh$\mathrm{.}24$FACTORYWinnipegSh$\mathrm{.}29$Sh$\mathrm{.}6$Sh$\mathrm{.}9$ Required The manufacturer wants to determine the optimal shipping schedule that will minimize transportation costs.RequiredFormulate the linear programming model for this problem. $[4$ Marks$]$Generate initial solution using Vogels Approximation Method and the Least Cost Method $[6$ Marks$]$Test the solution for optimality generated using the stepping stone Method $[10$ Marks$]$