The Sullivan brothers run a distribution company. They are responsible for transporting the product from three factories to four possible warehouses for a private company. The private company has already told them how much product each warehouse requires $($demand$)$ and how much each factory produces $($supply$).$ They$$ve been told it doesn$$t matter which factory supplies what warehouse, and warehouses can be supplied by multiple factories. The shipping costs are listed below. Since the brothers get paid the same amount no matter how they choose to ship, their goal is to minimize their costs $($thus increasing their profit$).$ Your goal is to setup the LP problem and solve the optimal schedule for the brothers.

To fill in the pink table next to Cost Function, you need to use the shipping costs from each factory to each warehouse given to you above.

If a good or$,$ in this case, factory$/$warehouse is involved, write down $1$ in the related cell, and $0$ otherwise. For example, to fill in cell E$19,$ think whether Factory A is involved in the case of A:$3($i$.$e$.,$ when the product is being transported from Factory A to warehouse $3).$ Since the answer is yes, we would write down $1$ in cell E$19.$

To fill in the green table $($Usage$),$ use SUMPRODUCT function. Note that the number of products transported from each factory to each warehouse should go into the yellow table $($you need to use Solver to find the optimum numbers$).$

Use SUMPRODUCT to fill in the Minimize Total Cost cell $($i$.$e$.,$ green cell$).$ Note that the costs come from the pink table $($one array in SUMPRODUCT$),$ and number of products transported from each factory to each warehouse comes from yellow table $($the other array in SUMPRODUCT$).$

Finally, use Solver to find the optimum values and minimum total transportation cost. Make sure you are adding proper constraints.