1 PM EDT OA manufacturer is considering alternatives for building new plants in
ID: 422989 • Letter: 1
Question
1 PM EDT OA manufacturer is considering alternatives for building new plants in order to be located closer to three of its primary customers with whom it intends to develop long-term relationships. The net cost of manufacturing and transporting capacity of the plant. These costs are summarized in the following table each unit of the product to its customers will vary depending on where the plant is built and the production Net Cost per Unit Plant 3 70 65 50 4 20 4525 5 65 4545 The annual demand for products from customers x, Y, and Z is expected to be 40,000, 25,000, and 35,000 units, respectively. The annual production capacity and construction costs for each plant are: Cost (in $1,000 $1,325 $1,100 $1,500 $1,200 $1,400 50,000 The company wants to determine which plants to build in order to satisfy customer demand at a minimum total cost. a. Select the correct 1LP model for this problem. Let Py represent Production at plant / allocated to meet demand for customer Let Yi represent 1 if any Xy 0, 0 otherwise. 65Psx + 45Psy+ 45Psz +1000 (1,325Y: +1,100Y2 + 65Psx + 45PsY +45Psz + 1000 (1,325Ys + 1,100Y2+Explanation / Answer
a. The correct ILP model for this problem is provided in option “IV”. The objective function and all the constraints are proper in this option.
b. Spreadhseet model:
Thus the answer is:
c. Total construction cost (This does not include cost of supplying to customers)
Cost of supplying to customers = $4,000,030
Total cost i.e. construction cost+cost of supplying = $7,825,030
Net cost Plant X Y Z Binary variable 1 35 30 45 Plant 2 45 40 50 1 1 3 70 65 50 2 1 4 20 45 25 3 0 5 65 45 45 4 0 5 1 Plant X Y Z 1 23106 16892 0 2 16894 3107 1 3 0 0 0 4 0 0 0 5 0 5001 34999 Total cost to supply to customers 4000030 Total construction cost 3825000 Total cost 7825030 Constraints 39998 <= 40000 20002 <= 30000 0 <= 0 0 <= 0 40000 <= 40000 40000 >= 40000 25000 >= 25000 35000 >= 35000Related Questions
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