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 the contract specifications state that the mix should contain a minimum of 30% sand. A total volume of 100,000 m² 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 construction engineer on the project, you are asked to determine how much material should be taken from each pit to minimize the total cost of mixed material. 

Find:

a) Formulate the problem with mathematical expressions for decision variables, objective function, and constraints.

b) Solve the problem using Excel Solver and determine the optimal volume of material transported from each pit and the total cost. 

c) Perform post-optimization sensitivity analysis using Excel Solver. Provide sensitivity report results and interpret these results regarding range of optimality and shadow price. 

d) If you had not been hired, the contractor would have used 60,000 m from Bloomingdale and 40,000 m from Valley Springs. How much did you save the company by giving them the expert's advice? (5)