A soda company owns three factories and supplies to four cities: Dallas, TX; For

Question

A soda company owns three factories and supplies to four cities: Dallas, TX; Fort Worth, TX; Oklahoma City, OK; and Tulsa, OK. The shipping costs per truckload together with the annual output of each factory and the annual demand of each city are given in transportation soda data.xlsx. Demand and output are both in units of truckloads.

Suppose that you are asked to determine the optimal shipping plan to minimize the total transportation cost, while exactly meeting the demand of each city, and not exceeding the capacity of any of the plants.

What are your constraints? Give an algebraic expression. Nonnegativity is a constraint here, but you don’t need to mention it explicitly, just make sure you check the box in Solver in the next question.

Sign in transportation_soda_data (B - Protected View - Excel AutoSaveO File Home Insert Page Layout Formulas Data Review View Help lell me what you want to do PROTECTED VIEW Be careful-files from the Internet can contain viruses. Unless you need to edit its safier to stay in Protected view. Enable Editing 83 Cost (S/Truckload) Factory 1 Factory 2 Factory 3 2 Dallas, TX 3 Fort Worth, TX 4 Oklahoma City, OK 5 Tulsa, OK 6 Annual Output 300 650 450 480 520 690 360 1130 390 315 280 250 660 780 420 Annual Demana 400 280 315 135 + 295% E- Data 49 9/19/2018 Type here to search

Explanation / Answer

Cost($/Truckload) Factory 1 Factory 2 Factory 3 Demand Dallas, TX 300 690 280 400 Fort Worth, TX 650 360 250 280 Oklahama City, OK 450 1130 660 315 Tulsa, OK 480 390 780 135 Annual Output 520 375 420 Let amount to be transported be Factory 1 Factory 2 Factory 3 Dallas, TX x11 x21 x31 Fort Worth, TX x12 x22 x32 Oklahama City, OK x13 x23 x33 Tulsa, OK x14 x24 x34 Objective is: Min 300x11+650x12+450x13+480x14+690x21+360x22+1130x23+390x24+280x31+250x32+660x33+780x34 The constraints are: Demand met x11+x21+x31 =400 x12+x22+x32 =280 x13+x23+x33=315 x14+x24+x34=135 Not exceed capacity x11+x12+x13+x14 < = 520 x21+x22+x23+x24

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