Please solve it manually & explain ! (ONLY C)

9.1-2. The Childfair Company has three plants producing child push chairs that are to be shipped to four distribution centers. Plants 1, 2, and 3 produce 12, 17, and 11 shipments per month, respec- tively. Each distribution center needs to receive 10 shipments per month. The distance from each plant to the respective distributing centers is given below: Distance Distribution Center 1 2 3 4 Plant 1 800 miles 1,300 miles 400 miles 700 miles 21,100 miles 1,400 miles 600 miles 1,000 miles 3 600 miles 1,200 miles 800 miles 900 miles The freight cost for each shipment is $100 plus 50 cents per mile. How much should be shipped from each plant to each of the distribution centers to minimize thc total shipping cost? (a) Formulate this problem as a transportation problem by con- structing the appropriate parameter table. (b) Draw the network representation of this problem. C (c) Obtain an optimal solution. Solution Given that The childfair company child push chains that four distribution centers. has three plants poradice to shipped to are Distance Distribution Center 1 2 3 0800 miles 4. 1,300 miles 400 miles 700 miles plant 2) 1,100 miles 1,400 miles 600 miles 1000 miles 3 Goomiles 1,200 miles 800 miles 900 miles The freight cost for each shipment $100plus 50 cents per mile. @ constouct the appropriate parameteu puoblem To calculate the total freight cast will be added to the shipment $100 with cost of total miles. Now, We have to draw the pasometea table. B E F Freight cost (8) Distribution Center 4 500 2 3 Production 1 750 300 500 12 plant 650 800 400 600 17 . 3 400 700 500 550 Demand o 10 10 10 The formula is used in the above table togetpadomeloa table A . E G Freight cast($) 1 12 Distribution Center 2 3 4 100+0:5X800 100+0:5*1300 10040-5*400 1000+05 * Soo 3.500 750 2) 300 looto:5X1100 100 +0:5X 1400 100+0.5*600 100 +0-5xloon => 650 800 - 400 2) 600 3.5X Goo Loo +0.5X 1200 100+0-5X800|100+0:5X ? 2 700 2).500 - 550 10 LO to 10 500 plant 2 3 17 ll 3 b Draw the network represent of this oldot problem transportation problem. as a Di 10 12 Pi 2 10 17 P2 Dz 10 11 P3 DU 10 Therefore The plants i plants 2 plants are sepsesented as Pi, P, and Ps And also having the distribution centers Di, Da , Dz and Dy. as lli