Sycamore Plastics (SP) is a manufacturer of polyethylene plastic pellets used as
ID: 340254 • Letter: S
Question
Sycamore Plastics (SP) is a manufacturer of polyethylene plastic pellets used as a raw material by manufacturers of plastic goods around the U.S. SP currently operates four manufacturing centers in Philadelphia, PA; Atlanta, GA; St. Louis, MO; and Salt Lake City, UT. The plants have different capacities and production costs as indicated in the table below. MAXIMUM CAPACITY (x 100,000 LBS.) PROD. COST PER 1,000 LBS.) Philadelphia 7.7 9.0 12.0 10.3 $320.00 $270.00 S300.00 $245.00 St. Louis Salt Lake City SP currently has six contract customers located in New York City; Birmingham, AL; Terre Haute, IN; Dallas, TX; Spokane, WA; and San Diego, CA. Transportation costs between the plants and various customers, as well as contracted demand from each customer, are shown in the table below. TRANSPORT COSTS PER 1,000 LBS BIRMINGHAM TERRE HAUTE DALLAS SPOKANE SAN DIEGO FROMTO Philadelphia NYC $45 S52 $56 58 $76 59 54 St. Louis Salt Lake City Total Demand 78 56 396 57 72 521 411 921 596 321 1,000 Ibs.) a. Create a solver model and find the optimal solution to help SP develop a distribution plan that will minimize costs to supply the customers' demand. (Enter your answers in terms of cost per 1,000 lbs and shipment quantities per 1,000 lbs. Round your answers to the nearest whole number.) CombinedCosts Per 1,000 lbs Terre Haute San Diego Philadelphia $ St. Louis Salt Lake City Solution (x 1,000 lbs NYC Terre Haute San Diego Philadelphia St. Louis Salt Lake CityExplanation / Answer
Let the quantities (in 1000 lbs) shipped from Philadelphia to NYC, Birmingham, Terre Haut….. San Diego be a1,a2,a3,a4,a5,a6.
Similarly other variables are shown below:
Combined cost = production cost+transport cost. Thus combined cost from Philadelphia to NYC = 320+45 = 365.
Thus the combine costs for all locations are shown below:
Thus total costs = 365a1+372a2+376a3+382a4+396a5+401a6+325b1+312b2+328b3+329b4+348b5+348b6+357c1+360c2+360c3+364c4+363c5+366c6+317d1+316d2+312d3+302d4+301d5+301d6
This is the objective function and has to be minimized. Constraints are:
The first 4 constraints are supply side constraints:
1. a1+a2+a3+a4+a5+a6<=770
2. b1+b2+b3+b4+b5+b6<=900
3. c1+c2+c3+c4+c5+c6<=1200
4. d1+d2+d3+d4+d5+d6<=1030
The next 6 constraints are demand side constraints:
5. a1+b1+c1+d1 = 521
6. a2+b2+c2+d2 = 411
7. a3+b3+c3+d3 = 921
8. a4+b4+c4+d4 = 596
9. a5+b5+c5+d5 = 321
10. a6+b6+c6+d6 = 396
Lastly all the variables should be >=0
The solution, as per excel's solver, is:
(in 1,000 lbs) From/To NYC Birmingham Terre Haute Dallas Spokane San Diego Philadelphia a1 a2 a3 a4 a5 a6 Atlanta b1 b2 b3 b4 b5 b6 St. Louis c1 c2 c3 c4 c5 c6 Salt Lake City d1 d2 d3 d4 d5 d6Related Questions
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