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.

Customer $1,2,3,4$

Demand $10025075300$

Facility

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.

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

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

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