Problem points$]$: Bertallo Classic produces tomato sauce at five different plants. The tomato

sauce is then shipped to one of three warehouses, where it is stored until it is shipped to one of the

company's four customers. The following inputs are provided in the two tables below:

$>$ The cost per ton of producing tomato sauce at each plant and shipping it to each warehouse.

$>$ The fixed annual cost of operating each plant and warehouse.

$>$ The plant capacities $($in tons$).$

$>$ The cost of shipping a ton of sauce from each warehouse to each customer.

$>$ The demands of four customers for tomato sauce $($in tons$).$

Bertallo Classic needs to decide which of the plants and warehouses to open, and which routes from

plants to warehouses and from warehouses to customers to use. All customer demands must be met. A

given customer's demand can be met from more than one warehouse, and a given plant can ship to

more than one warehouse. The objective is to minimize the company's total costs.

a$)$ Define the decision variables clearly and write down the detailed mathematical formulation

of Bertallo Classic's optimization problem.

$[15$ points$]$

b$)$ Solve the optimization problem with Excel Solver. Write down the optimal production and