Problem $2(75$ points$)$: Facilities Layout Problem

The following questions are associated with the facilities layout problem shown below.

The problem contains three plants supplying four customers or warehouses.

$\backslash$table$[[$Customer$,1,2,3,4,,],[$Demand$,100,250,75,300,,],[$Facility$,,,,,,],[1,10,5,12,20,1000,500],[2,12,7,24,15,2000,300],[3,23,9,7,18,1000,500]]$

Recall that refers to the cost associated with servicing customer from facility $.$ A solution refers to the amount of product that flows to customer from facility. You are given the following solution: $,,,,$ and all other $.$ Please answer the following questions.

Objective Function: Use the solution and the information found in to find the value of the objective function.

Capacity Constraint: Use the information contained in the Facility Layout Problem and solution to verify that the capacity constraints are not violated.

Demand Constraint: Use the information contained in the Facility Layout Problem and solution to verify that the customer demand constraints are satisfied.