Question

Question 5-8

of $1000 per million kWh. The network is not linked to city 3, however. The utility com- pany wishes to determine the most economical plan for the distribution and purchase of additional energy (a) Formulate the problem as a transportation model. (b) Determine an optimal distribution plan for the utility company (e) Determine the cost of the additional power purchased by each of the three cities Solve Problem 5-6, assuming that there is a 10% power transmission loss through the network. 5-7 5-8. Three refineries with daily capacities of 6,5, and 8 million gallons, respectively, supply three distribution areas with daily demands of 4,8, and 7 million gallons, respectively Gasoline is transported to the three distribution areas through a network of pipelines The transportation cost is 10 cents per 1000 gallons per pipeline mile. Table 5.26 gives the mileage between the refineries and the distribution areas Refinery 1 is not connected to distribution area 3 (a) Construct the associated transportation model. (b) Determine the optimum shipping schedule in the network. *5-9. In Problem 5-8, suppose that the capacity of refinery 3 is 6 milion gallons only and that distribution area 1 must receive all its demand. Additionally, any shortages at areas2 and 3 will incur a penalty of 5 cents per gallon. (a) Formulate the problem as a transportation model. (b) Determine the optimum shipping schedule. 5-10. In Problem 5-8, suppose that the daily demand at area 3 drops to 4 million gallons. Surplus production at refineries 1 and 2 is diverted to other distribution areas by truck The transportation cost per 100 gallons is $1.50 from refinery 1 and $2.20 from refinery 2 itar t itu urnlus productien to other chemical processes within the plant.

Answer 1

Solution Siven thot Thee refirer es oth chily cap cities 어 6.5 and 8 million galloons vespectvey Teediskibuion aeas coih dily demaneds ot 8and The. +horsporartion Cost is to cents per too gallons per pipeline mile Ris rot connected to distibutron area The X s he the antty ol gasole to be suplted fom telinery to h area and cy be the ine correspondiny th Cost of ars gabons calculatedbiptging the Cast er mle wtthe number of miles Carried re objectile i5 to minimize total cost of IransporationDouble Summatton 4 The marx fox tans poraon poblem is as folows

2. Ca) construct the assoctated asporotaton model Table will be shon beloo Transportation Per looo galloons Area Area Ara 3 Suply 6coo 8 5000 12 8000 18 lo 25 000 800 oo ne efinery 30 3 yThe total deandTotal supply Hence, Balanced hansportartion problem irth the to area 3 and othex nomal dermand and supply Conslant b Determine the optum shipping s rnun schedule t eluork rea2 Area3 Total re 2. 5000 00 So00 Sooo lalue of objeciVefun 2.

The e trrery i Aquru the demand of araltri lion) of area 2 C2 millan and parctialty demand of area 2 (2 miltion elirery coitl Sugply to aea 2 (5 mitlin) Reltnery 3upply to ae miltion) and to atkea Radtaltly demand 3 (t million Thexefore The total minioum cost of arfor-tatton ts 2431000