An electric car company owns two facilities that manufacture and supply high-capacity lithium-ion batteries to three vehicle assembly plants. The first battery facility can produce and ship up to 10,000 lithium-ion batteries per month, and the second facility can produce and ship up to 8,000 batteries per month. The per-unit shipping cost and the battery demand from the three assembly plants are provided in the following table. 

a. Formulate and solve an IP model to determine the number of batteries to be shipped from each manufacturer to the three assembly plants. What is the lowest shipping cost that the electric car company would incur?

b. How many batteries should the company ship from each manufacturer to each of the three assembly plants in order to minimize the shipping cost?

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Shipment Cost per Battery Plant 1 Plant 2 Plant 3 $15.67 $12.30 $13.55 $13.75 $13.90 $14.00 5,000 6,600 6,400 Manufacturer 1 Manufacturer 2 Monthly Demand