For construction of a civil engineering facility a contracto

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. Define the decision variables Write the constraints in mathematical form Write the objective function in mathematical form Find the optimum solution using the graphical method (how much material should the contractor take from each pit in order to minimize the overall cost of the material?) If you had not been hired, the contractor would have used 60,000 m3 from Bloomingdale and 40,000 m3 from Valley Springs. How much did you save the company by giving them the expert\'s advice as your answer to Question (d)?

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