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Posted: January 29th, 2023
Question 1.A manufacturing firm located in Chicago ships its product byrailroad to Detroit. Several differ- ent routes are available, asshown in the following diagram, referred to as a network:Each circle in the network represents a railroad junction. Eacharrow is a railroad branch be- tween two junctions. The numberabove each arrow is the cost ($1,000s) necessary to ship 1 ton ofproduct from junction to junction. The firm wants to ship 5 tons ofits product from Chicago to Detroit at the minimum cost.3.Formulate a linear programming model for thisproblem.3. Solve the model by using the computer.Question2.A tailor makes wool tweed sports coats and wool slacks.He is able to get a shipment of150square yards of wool cloth from Scotland each month to make coats and slacks, andhe has 200hours of his own labor to make them each month. A coat requires 3 squareyardsof wool and 10hours to make, and a pair of pants requires 5 square yards of wool and 4hours to make.Heearns $50 in profit from each coat he makes and $40 from each pair ofslacks. He wants to knowhow many coats and slacks to produce to maximize profit.a.Formulate an integer linear programming model for this problem.b.Determine the integer solution to this problem using the computer.Compare thissolution to the solution without integer restrictions and indicate if the roundeddown solutionwould have been optimal.Question 3.Construct an Excel simulation for the total profit function defined as follow:Profit = Total revenue â Fixed cost â Variable costWhere,Total revenue = p.xFixed cost = FVariable cost = v.xAndP = Price of the productV = Variable cost per unitVariable cost = v.xFor this problem, assume that :-F has an equal likelihood discrete distribution with three values : [$1000, $3000,$5000]V is normally distributed with a mean of 10 and a standard deviation of 2P is uniformly distributed over the range [150, 200]x is normally distributed with mean 100 and a standard deviation of 15Construct the Simulation in Excel with 1000 replications. Construct a histogram of Profit.Calculate and report average Profit.
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