Problem $1$: Cost Trade$-$offs in Transportation

A company needs to transport goods from a warehouse to three different cities. The transportation costs per unit to City

A$,$ City B$,$ and City C are $$100,$$$150,$ and $$200,$ respectively. The demand for goods is $500$ units for City A$,300$ units for

City B$,$ and $200$ units for City C$.$ The company has a budget constraint of $$120,000.$ How many units can be transported to

each city while adhering to the budget constraint?

Problem $2$: Transportation Cost Minimization

Scenario: A logistics company has to transport $1,000$ units of goods from two warehouses $($W$1$ and W$2)$ to two

destinations $($D$1$ and D$2).$ The transportation costs from W$1$ to D$1$ and D$2$ are $$4$ and $$6$ per unit, respectively. From W$2,$

the costs are $$5$ and $$7$ per unit. W$1$ has a capacity of $600$ units and W$2$ has a capacity of $500$ units.

Question: Formulate a transportation cost minimization problem and solve for the optimal number of units to be

transported from each warehouse to each destination.