You are the manager of a civil engineering pavement company that makes concrete for various highway...

 

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You are the manager of a civil engineering pavement company that makes concrete for various highway projects in the State of Texas. Your company has various sites across the state to take sand and gravel materials necessary to make a concrete mix used in pavement projects. For a construction job near Prairie View, Texas, there are two sites to extract sand and gravel raw materials: a) North-town and b) South-town. Due to variations in the soil properties at each site, the raw material from North-town produces 43% sand and 57% gravel. The raw material from South-town produces 55% sand and 45% gravel. The construction job in Prairie View requires a minimum of $3,000 cubic meters of sand and gravel mix. The pavement design requires a minimum of 25,000 cubic meters of sand and no more than 38,000 cubic meters of gravel in making the concrete mix for this highway job. The unit delivery costs (includes the cost of raw materials and the hauling costs) are $120 and $130 per cubic meter from North-town and South-town, respectively. a) Formulate this problem as a linear programming problem whose solution will enable you to minimize the cost. Clearly state the objective function and the constraint equations of the problem. [30 points] b) Solve the LP model by using LINDO and show the LINDO output for this LP in addition to the report of Objective Coefficient Ranges and Righthand Side Ranges. [30 points] c) Suppose that you decide to change the specification of the concrete mix to achieve higher durability against repeated vehicle load cycles. By using your ethical and professional responsibilities as a civil engineer, how much can you change the quantities of sand and gravel that needed for your job without any increase in your cost, and why? [40 points] You are the manager of a civil engineering pavement company that makes concrete for various highway projects in the State of Texas. Your company has various sites across the state to take sand and gravel materials necessary to make a concrete mix used in pavement projects. For a construction job near Prairie View, Texas, there are two sites to extract sand and gravel raw materials: a) North-town and b) South-town. Due to variations in the soil properties at each site, the raw material from North-town produces 43% sand and 57% gravel. The raw material from South-town produces 55% sand and 45% gravel. The construction job in Prairie View requires a minimum of $3,000 cubic meters of sand and gravel mix. The pavement design requires a minimum of 25,000 cubic meters of sand and no more than 38,000 cubic meters of gravel in making the concrete mix for this highway job. The unit delivery costs (includes the cost of raw materials and the hauling costs) are $120 and $130 per cubic meter from North-town and South-town, respectively. a) Formulate this problem as a linear programming problem whose solution will enable you to minimize the cost. Clearly state the objective function and the constraint equations of the problem. [30 points] b) Solve the LP model by using LINDO and show the LINDO output for this LP in addition to the report of Objective Coefficient Ranges and Righthand Side Ranges. [30 points] c) Suppose that you decide to change the specification of the concrete mix to achieve higher durability against repeated vehicle load cycles. By using your ethical and professional responsibilities as a civil engineer, how much can you change the quantities of sand and gravel that needed for your job without any increase in your cost, and why? [40 points]