FIU Labor and Equipment in Civil Engineering System Questions

Problem 1  For a certain civil engineering system, we have two types of  resources: Labor, and equipment We refer to these resources by the index  j. Likewise each resource can be assigned to two types of  activities: Maintenance and operations. We refer to these activities by  the index i. Furthermore, the variables xij represent the amount of hours used by the resource j (labor/equipment) performing activity i (maintenance/ operations).Maintenance.   Maintaining the system involves the use of equipment and labor.The part of the labor that goes into maintenance has a cost of  $2/hour; and the part of equipment use that goes into maintenance has a  cost of $4/hour. The total labor and equipment costs for maintenance should not exceed the maximum maintenance budget of $21 millionOperations.      Operating the system involves the use of equipment and labor.The part of labor that goes into operations has a cost of $5/hour;  and the part of equipment use that goes into operations has a cost of  $3/hour. The total labor and equipment costs for operations should not exceed and maximum operations budget of $18 millionFrom past records of similar systems, it has been found that the performance of the system, Z,  depends on the amount of effort put in maintenance and operations.  Specifically, each hour of labor represents $3 million of profit for the  company and each hour of equipment represents $2 million of profit for  the company (it does not matter whether these hours where used for  maintenance or operation). As a manager in the agency, you seek to  maximize Z under the given budgetary constraints.Write the complete optimizations problem mathematically (the objective function and all constraints).Problem 2 For construction of a civil engineering facility, a contractor has  found natural reserves of sand and gravel at Bloomingdale and Valley  Springs where he may purchase such material. The unit cost including  delivery from Bloomingdale and Valley Springs is $5 and $7,  respectively. After the material is brought to the site it is mixed  thoroughly and uniformly, and contract specification state that the mix  should contain a minimum of 30% sand.A total volume of 100,000 m3 of mixed material is needed  for the project. The Bloomingdale Pit contains 25% sand and the Valley  Springs Pit contains 50% sand.As the new young construction engineer on the project, you are asked  to determine how much material should be taken from each pit in order to  minimize the cost of material.