1. The CFO for the Shelton Corporation has $1.2 million to allocate to the following budgetrequests from five departments:Dept. 1 : $450,000Dept. 2: $310,000Dept. 3: $275,000Dept. 4: $187,500Dept. 5: $135,000Because the total budget requests exceed the available $1.2 million, not all the requestscan be satisfied. Suppose the CFO considers the requests for departments 2 and 3 to betwice as important as those from departments 4 and 5, and the request from department1 to be twice as important as those from departments 2 and 3. Further, suppose theCFO wants to make sure each department receives at least 70% of the request amount.*Formulate a Goal Programming model for this problem.2. The owner of the Weiner-Meyer meat-processing plant wants to determine the bestblend of meats to use in the next production run of hamburgers. Three sources of meatcan be used. The following table summarizes the relevant characteristics of thesemeats:Cost per Pound% Fat% Protein% Water% FillerMeat 1$0.7515%70%12%3%Meat 2$0.8710%75%10%5%Meat 3$0.985%80%8%7%A local elementary school has ordered 500 pounds of meat for $1.10 per pound. Theonly requirement is that the meat consist of at least 75% protein and at most 10% eachof water and filler. Ordinarily, the owner would produce the blend of meats that achievedthis objective in the least costly manner. However, with the concern of too much fat inschool lunches, the owner also wants to produce a blend that minimizes the fat contentof the meat produced.*Formulate an Multiple Objective Linear Programming model for this problem.* Implement your formulation in a spreadsheet, and individually optimize the twoobjectives under consideration.* How much profit must be forfeited in order to fill this order using the mix that minimizesthe fat content?* Solve this problem with the objective of minimizing the maximum percentage deviationfrom the target values of the goals. What solution do you obtain?* Assume the owner considers minimizing the fat content twice as important asmaximizing profit. What solution does this imply?3. The PENTEL Corporation manufactures three different types of computer chips. Eachtype of chip requires different amounts of processing time in three different departmentsas summarized in the following table.Processing Hours Required per 100 chipsChip AChip BChip CDept. 1Dept. 2Dept. 3323244432HoursAvailable10,0009,00011,000The total profit for each type of chip may be described as follows:Chip A profit = -0.35A2 + 8.3A + 540Chip B profit = -0.60B2 + 9.45B + 1108Chip C profit = -0.47C2 + 11.0C + 850Where A, B, and C represent the number of chips produced in 100s.* Formulate an Nonlinear Programming model for this problem.* Implement your model in a spreadsheet and solve it.* What is the optimal solution?4. The Major Motors Corporation manufactures heavy trucks at a plant in Dublin, Virginia.The factorys stock of spare and custom parts is stored in a huge shelving system that isseveral stories high and runs the length of several football fields. An automated cherrypicking vehicle runs back and forth along a shelving unit and is able to simultaneouslyraise or lower to any height to pick needed stock items from the various bins in theshelving unit. Each bin in the shelving unit is of equal size and is identified by a specificrow and column number. Typically, each run the cherry picker makes involves visitingseveral different bins to retrieve various parts. To help minimize operating costs, thecompany wants to develop a system to determine the most efficient way for the cherrypicker to visit each required bin site before returning to its initial position. As an example,suppose the cherry picker needs to retrieve 10 parts stored in the following bin locations.Part12345678910Row31412020283011710Column272213316123119325Assume the cherry picker must start and finish at row 0 and column 0.* Use a spreadsheet to compute the straight-line distance between each pair of binlocations.* Use Solvers evolutionary algorithm to determine the shortest tour for the cherry pickerto follow.* What is the best tour you can find?