Minimization Problem $3$: Minimizing Transportation Costs for a Logistics Company

A logistics company is responsible for transporting goods from two warehouses $($W$1$ and W$2)$ to two retail stores $($S$1$ and S$2).$ Each warehouse has a specific supply capacity, and each store has a specific demand requirement. The transportation cost per unit varies depending on the route:

Transporting one unit from W$1$ to S$1$ costs $$4.$

Transporting one unit from W$1$ to S$2$ costs $$6.$

Transporting one unit from W$2$ to S$1$ costs $$5.$

Transporting one unit from W$2$ to S$2$ costs $$3.$

The available supply at each warehouse is:

W$1$: $50$ units.

W$2$: $70$ units.

The demand at each store is:

S$1$: $60$ units.

S$2$: $60$ units.

The company$$s objective is to minimize the total transportation cost while ensuring that the supply from the warehouses meets the demand at the stores.

Question:

a$)$ Using the graphical linear programming method, determine the minimum transportation cost and the optimal transportation plan $($i$.$e$.,$ how many units should be transported from each warehouse to each store$).$