(a) Write the linear programming (LP) model that could be used to find the best solution (clearly define the decision variables and any other notations you use in your model, show the necessary set of algebraic expressions for the constraints and the objective function, and label the units and the purpose of each constraint and the objective function) (b) Use an LP software to solve your model and submit the input file you used (c) Write out the final solution 5-19. A landowner has decided to develop a piece of property and has hired a developer to manage the project. Land clearing and grubbing operations are completed and one of two bridges on the property is completed. The second bridge will be completed in 6 weeks. An engineering firm has been engaged by the developer to do all design work as well as perform all necessary field services and quality control of all construction operations. The engincering design requires fill to be placed, and spread by bulldozer, in the three areas shown on the plot plan for Exercise 5-19. One bulldozer is presently assigned to each fill area. Fill is available from suppliers 1,2 , and 3 at a cost of $1.25/yd3 at a distance up to 5mi. Any hauling distance beyond 5mi will incur an additional cost of 5.05/yd3/mi. Supplier 4 would have to lease trucks to supply the site (up to six trucks maximum) and charges a flat rate of $2.00/yd3. Each bulldozer can handle a maximum of 8 trucks /hr, dumping fill. Each truck has a capacity of 10yd3. (a) Develop a model that could be used to find the minimum cost way of meeting the fill requirements if the bridge under construction was not finished. (b) Develop a model that could be used to find the minimum cost way of meeting the fill requirements if the bridge under construction was in place. Fill requirements \begin{tabular}{cr} \hline Site & \multicolumn{1}{c}{y3} \\ \hline 1 & 120,000 \\ 2 & 100,000 \\ 3 & 80,000 \end{tabular} Fill supply \begin{tabular}{ccc} \hline Borrowpit & y3available & Trucksavailable \\ \hline 1 & 60,000 & 4 \\ 2 & 40,000 & 4 \\ 3 & 180,000 & 10 \\ 4 & 100,000 & 6 \end{tabular}