v2.cengagenow.com C + 88 My Home C CengageNOWv2 | Online teaching and learning resource from Cengage Learning Course Hero Topic 5 - Linear Programming: Distril Problem 10-03 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 From Hamilton Butler Clermont Southern Gas 10 20 15 Northwest Gas 12 15 18 a. Choose the correct network representation of this problem. (ii) Hamilton 10 Hamilton 12 300 400 12 10 Southern 500 Southern 1 1 500 15 15 Butler Butler 2 200 2 200 20 Northwest Northwest 2 400 2 400 400 300 Clermont Clermont 18 3 15 (iii) (iv) Hamilton 400 Hamilton 300 1 1 10 10 500 Southern 20 500 Southern 20 1 15 12 Butler 200 Butler 12 2 2 200 15 Northwest Northwest 400 400 18 2 18 Previous Assignment Score: 0.0% All work saved. Save and Exit Submit Assignment for Gradingv2.cengagenow.com C + 88 My Home C CengageNOWv2 | Online teaching and learning resource from Cengage Learning Course Hero Topic 5 - Linear Programming: Distril 15 15 400 Northwest 2 18 400 Northwest 2 18 Clermont 300 Clermont 3 400 b. Develop a linear programming model that can be used to determine the plan that will minimize total distribution costs. Let xij = amount shipped from supply node / to demand node j. Min x11 + x12 + + SIX x21 + * 22 + X23 s.t. x11 + X12 + X13 *21 + * 22 + *23 S X11 *21 11 11 11 IA WA 1+ + X22 X13 + X23 = xij 2 0 for all i, j 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 d. Recent residential and industrial growth in Butler County has the potential for increasing demand by as much as 100 units. Which supplier should Tri-County contract with to supply the additional capacity? Previous Assignment Score: 0.0% All work saved. Save and Exit Submit Assignment for GradingSafari File Edit View History Bookmarks Window Help C G Q 8 @ Fri Sep 2 12:52 AM .. . v2.cengagenow.com C + 188 LL' My Home C CengageNOWv2 | Online teaching and learning resour.. Homework Help - Q&A from Online Tutors - Course H. creen Shot Screen Shot Screen Shot Documents Topic 5 - Linear Programming: Distril -0...34.27 PM 2022-0....50.17 PM 2022-0...34.02 AM ? *21 + *22 + X23 S X11 + * 2 creen Shot Screen Shot Screen Shot quantitative X12 1 + X22 -0....34.19 PM 2022-0....35.11 PM 2022-0...26.50 AM methods.xisx X13 X23 = Xij 2 0 for all i, j c. Describe the distribution plan and show the total distribution cost. creen Shot Screen Shot Screen Shot Screen Shot -0....34.13 PM 2022-0....35.07 PM 2022-0...26.40 AM Amount Cost 2 Southern - Hamilton Southern - Butler creen Shot Screen Shot Screen Shot Screen Shot Southern - Clermont -0...34.07 PM 2022-0....35.01 PM 2022-0...26.26 AM 2022-0...50.39 AM Northwest - Hamilton Northwest - Butle ty Northwest - Clermont creen Shot Screen Shot Screen Shot Screen Shot Total Cost -0...34.02 PM 2022-0...34.56 PM 2022-0...22.33 AM 2022-0...50.22 AM d. Recent residential and industrial growth in Butler County has the potential for increasing demand by as much as 100 units. Which supplier should Tri-County contract with to supply the additional capacity? Amount Cost creen Shot Screen Shot Screen Shot Screen Shot 4 :-0...33.55 PM 2022-0...34.47 PM 2022-0....22.16 AM 2022-0...46.07 AM Southern - Hamilton $ Southern - Butler Southern - Clermont creen Shot Screen Shot Screen Shot Screen Shot Northwest - Hamilton -0...33.53 PM 2022-0...34.43 PM 2022-0....21.57 AM 2022-0...46.03 AM Northwest - Butler Northwest - Clermont Total Cost creen Shot Screen Shot Screen Shot Screen Shot -0...33.48 PM 2022-0...34.39 PM 2022-0....21.56 AM 2022-0...45.52 AM From the new solution we see that Tri-County should contract wit v Gas for the additional 100 units. Southern Northwest Previous creen Shot Screen Shot Screen Shot Screen Shot -0...33.43 PM 2022-0...34.33 PM 2022-0....11.39 PM 2022-0...45.35 AM Assignment Score: 0.0% All work saved. Save and Exit Submit Assignment for Grading