Question $1$

$(25$ marks$)$

The $\frac{C}{O}O$ has recognised that the high cost of transportation from their manufacturing plants to their warehouses has been part of the main reason the company is losing money. The company currently has $3$ manufacturing plants. Plant $1$ manufactures $35$ cars to ship, plant $2$ manufactures $50$ and plant $3$ manufactures $20$ cars to ship per month.

The cars are shipped to $4$ warehouses to store before being sold. Warehouses $1,2,3$ and $4$ can store up to $45,20,30$ and $30$ cars respectively. You are tasked with the following:

a$)$ Use the Northwest Corner algorithm to find the initial feasible solution to the problem above.

$(10$ marks$)$

b$)$ Use the stepping stone method to check whether the solution is optimal

$(6$ marks$)$

c$)$ Complete one iteration of the stepping stone method to check whether the solution in b$)$ is correct

$(9$ marks$)$