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You Doll & Doll has two facilities that source, procure raw material, manufacture, QAQC and initial Pack for delivery. The company distributes the toys from

You Doll & Doll has two facilities that source, procure raw material, manufacture, QAQC and initial Pack for delivery. The company distributes the toys from these two plants through two distribution centers (DCs) located at Wah & Jhelum, to three different customer regions namely, Islamabad, Rawalpindi, Lahore where the toys are packaged as per demand and sold.

Each plant has a maximum capacity for its weekly supply of toys. Likewise, each region has a minimum weekly demand for toys. Furthermore, distributer has asked to sell toys at their facility calling it factory outlets, so they havedemands as well. The cost to distribute a pallet of toys (100 toys per pallet) between each plant and region depends on the distances between them. The transportation costs, maximum supplies in the plants, and minimum demands intheregionsaresummarizedinthefollowingtables:

Origin Plant

Destination DC

Transportation Cost (Rs/Pallet of toys )

Plant 1

Wah

5600

Jhelum

4100

Plant 2

Wah

5200

Jhelum

4200

Origin DC

Destination Region

Transportation Cost (Rs/pallets of toys)

Wah

Lahore

7900

Rawalpindi

5200

Islamabad

4200

Jehlum

Lahore

4700

Rawalpindi

6500

Islamabad

6700

Plant

Maximum Supply (pallets of toys)

Plant 1

1300

Plant 2

1050

Region

Minimum Demand (pallets of toys)

Lahore

500

Rawalpindi

1000

Islamabad

350

Wah

100

Jhelum

150

In order to minimize total costs, Doll & Doll wishes to optimize the flow of toys from plants to DCs to regions to customers.

  1. In the optimal solution, what is the minimum total cost of moving the toys from plant toDCs?
  2. WhatistotaltransportationcostofmovingthetoysfromDCstoregions?
  3. What is total transportation cost of moving the toys from plant toregions?

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