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esource from Cengage Learning- Microsoft Edge ssignmentMan.doinvoker-assignments& takeAssignment es lor Locator-ass gr ment-take&r pro signmen take ress- se Calculator Problem 6-03 Tri-County Utilities, Inc., supplies natural gas to customers in a three-county area. The company purchases natural gas from two companies Southern Gas and Northwest Gas. Demand forecasts for the coming winter season are as follows: Hamilton County, 400 units; Butler County, 200 units; and Clermont County, 300 units. Contracts to provide the following quantities have been written: Southern Gas, 500 units; and Northwest Gas, 400 units. Distribution costs for the counties vary, depending upon the location of the suppliers. The distribution costs per unit (in thousands of dollars) are as follows: To Clermont 15 18 Hamilton Butr From Southem Gas Northwest Gas 10 12 20 15 a. Choose the correct network representation of this problem. Hamalton 12 Hamilton 10 300 12 400 10 Southem 500 Southern 500 15 Butler Butler 200 200 20 20 Northwest Northwest 400 400 Previous rce from Cengage Learning- Microsoft Edge invoker= assignments&takeAssignmentsessionLocator= assignment-take&inprogress=false ment/takeAssi Calculator elop a linear programming model that can be used to determine the plan that will minimize total distribution costs. xy = amount shipped from supply node i to demand node j. 15 X22+ 12 x21+ 15 X13+ Min s.t. 1 X13 X1리+ 1 1 X11 1x22 1 X21 1 X11 1 X22 1 X12 1 X13 Xij 2 0 for all i, j e the distribution plan and show the total distribution cost. Amount Cost Southern Hamilton Southern Butler Southern - Clermont 2000 200 4500 300 m Cengage Learning- Microsoft Edge takeAssignmentMain.do?invoker= assignments&takeAssignmentsession ocator=assignment-take&nprogresstalse Calculator c. Describe the distribution plan and show the total distribution cost. Amount Cost Southern Hamilton Southern Butler Southern Clermont Northwest Hamilton Northwest Butler Northwest Clermont Total Cost 2000 200 300 200 200 4500 2400 3000 Recent residential and industrial growth in Butler County has the potential for increasing demand by as much as 100 units. W should Tri-County contract with to supply the additional capacity? Amount Cost Northwest Hamilton Northwest Butler Northwest Clermont Total Cost 200 2400 200 3000 d. Recent residential and industrial growth in Butler County has the potential for increasing dernand by as much as 100 units. Which supplier should Tri-County contract with to supply the additional capacity? Amount Cost Southern Hamilton Southern Butler Southern - Clermont Northwest Hamilton Northwest Butler Northwest-Clermont Total Cost From the new solution we see that Tri-County should contract with ▼ Gas for the additional 100 units. (Pre Previous ammu Email Instructor Save and Exit Submit Test for Grading All work saved

Answer 1

Date: ---27/04/2019 Answer. a) Hamilton 1 400 10 20 Southern 15 Butlr 200 12 2 15 400 Northwest 2 18 Clermont 300 Supplies Demands

! b) riable xyz amount of x units shipped from supply node y to demand node z. x11-Units shipped from supply node "Southern" to demand node "Hamilton." x12Units shipped from supply node "Southern" to demand node "Butler." x13Units shipped from supply node "Southern" to demand node "Clermont." x21Units shipped from supply node "Northwest" to demand node "Hamilton." x22Units shipped from supply node "Northwest" to demand node "Butler." x23 = Units shipped from supply node "Northwest" to demand node "Clermont." Objective Function - Minimize total distribution costs; Min = 10#x11 + 20*x12 + 15#x13 + 124x21 + 15*x22 + 18*x23; !Constraints; x11 + x12 + x13 <= 500; x21 + x22 + x23 <= 400; ! Southern supply capacity; Northwest supply capacity: Hamilton demand forecast, Butler demand forecast; !Clermont demand forecast; x11 + x21 400; x12 + x22 = 200; x13 + x23 = 300; x11 >= 0; !cannot be less than 0; x12 >= 0; x13 >- 0; x22 >- 0 x23 0

Global optimal solution found Objective value: Infeasibilities: Total solver iterations: 11900.00 0.000000 Variable X11 X12 X13 X21 X22 X23 Value 200.0000 0.000000 300.0000 200.0000 200.0000 0.000000 Reduced Cost 0.000000 7.000000 0.000000 0.000000 0.000000 1.000000 Amount 200 300 200 200 Cost Southern Hamilton Southern- Clermont Northwest Hamilton Northwest - Butler $2000 4500 2400 3000 $11,900 Total Cost

d) Butler County demand is increasing by 100 units, so we change our Butler demand in LINGo from 200 to 300. x12 x22-300; Butler demand forecast: To decide what company (Southern Gas or Northwest Gas) is best suited to provide this increase, we increase the supply at each company in LINGO by 100 x11 + x12 + x13 <= 600; ! Southern supply capacity; x21 + x22 x23< 500 Northwest supply capacity;