Please read the instructions! Instructions: I will not answer any questions. If you think there is a typo or a mistake in the questions, just make an assumption (state your assumption) and solve the question based on that. Type your answers. For modeling questions, clearly dene your variables. Briey explain the meaning of the con- straints. For modeling questions, write your optimization models clearly together with the objective function, constraints and variable types. If the question says solve, copy and paste the ampl output. Display your decision variable values and objective function value. In ampl questions, paste your model and data les in your answer report. Do not send separate les. Do your best. Good luck! 1. (25 points) Three dierent items are to be processed through three machines. Each item must be processed rst on machine 1, then on machine 2, and nally on machine 3. The sequence of items may dier for each machine. Assume that the times tij required to perform the work on item i by machine j are known and are integers. Our objective is to minimize the total time necessary to process all the items. (a) Formulate the problem as an integer programming problem. (b) Design a simple instance with two items and two machines. Set processing times (choose small values) for items on machines. Write your model in AMPL and test the correctness of your model. Discuss (you may demonstrate the solution on a gure) whether your solution is feasible or not. 2. (25 points) Consider a special knapsack problem. A housewife goes to shopping. There are N items in the store. Each item k would bring a value pk to the shopping. If she decides to shop, she can buy one shopping bag with a capacity B and a xed cost of C. If she buys the bag, she needs to pay C but then she can have capacity B to buy items. Each item k needs space bk in the bag. She wants to decide which items to buy with maximum value. Note that you 1 IE528 Mathematical Programming and Modeling You need to work…