I ONLY NEED QUESTION 3 ANSWERED, I ONLY NEED QUESTION 3 ANSWERED, I ONLY NEED QUESTION 3 ANSWERED
I ONLY NEED QUESTION 3 ANSWERED, I ONLY NEED QUESTION 3 ANSWERED
2. The Versatech Corporation has decided to produce three new products. Five branch plants now have excess production capacity. The unit manufacturing cost of the first product would be $31, $29, $32, $28, and $29 in Plants 1, 2, 3, 4, and 5, respectively. The unit manufacturing cost of the second product would be $45, $41, $46, $42, and $43 in Plants 1, 2, 3, 4, and 5, respectively. The unit manufacturing cost of the third product would be $38, $35, and $40 in Plants 1, 2, and 3, respectively, whereas Plants 4 and 5 do not have the capability for producing this product. Sales forecasts indicate that 600, 1000, and 800 units of products 1, 2, and 3, respectively, should be produced per day. Plants 1, 2, 3, 4, and 5 have the capacity to produce 400, 600, 400, 600, and 1000 units daily, respectively, regardless of the product or combination of products involved. Assume that any plant having the capability and capacity to produce them can produce any combination of the products in any quantity. (a) (points: 3) Write down an optimization formulation for this problem. Remark: This is different from the previous problem. In this problem, you need to write down the abstract optimization formulation, explain the meaning of each optimization variable and explain what are the data. (b) (points: 1) There is no "transportation" in the problem statement (there is no "truck, no "route"). Nevertheless, the formulation is similar to a transportation problem. Ex- plain how to view this problem as a transportation problem. (c) (points: 2) Solve the problem and report the optimal solution and optimal cost. You can use software to solve the problem; if so, please provide the code (e.g. copy the code to the solution file, or take a snapshot and paste the picture in the solution file). If you do no attach the code to your solution, you will have zero points for this problem. 3. Reconsider the scenario in Problem 2. Suppose that the sales forecasts have been revised downward to 240, 400, and 320 units per day of products 1, 2, and 3, respectively, and that each plant now has the capacity to produce all that is required of any one product- except plants 4 and 5 which still cannot produce the third product. Therefore, management has decided that each new product should be assigned to only one plant and that no plant should be assigned more than one product (so that three plants are each to be assigned one product, and two plants are to be assigned none). The objective is to make these assignments so as to minimize the total cost of producing these amounts of the three products. (a) (points: 3) Write down an optimization formulation for this problem. Remark: This is different from the previous problem. In this problem, you need to write down the abstract optimization formulation, explain the meaning of each optimization variable and explain what are the data. Hint: Formulate this problem as an assignment problem and construct the appropriate cost table. This makes it easier to explain. 2 (b) (points: 3) Solve the problem and report the optimal solution and optimal cost. You can either use AMPL or Excel to solve the problem; if so, please provide the code or excel sheet (e.g. copy the code to the solution file, or take a snapshot and paste the picture in the solution file). If you use other methods or do no attach the code (or excel sheet) to your solution, you will have zero points for this
