Problem 1 (35 pt)

Bowman & Kinkins (B&K) is a hi-fi speaker manufacturer. They proudly engineer and manufacture their speakers in the United Kingdom. To celebrate their 75-year anniversary, they will release a Limited Edition of their most well-known speakers from the acclaimed 6000 Series, the floorstanding speaker B&K 6003.

B&K has three manufacturing plants in the UK (Manchester, Edinburgh, Southampton) that will be in charge of producing a first batch of these hi-fi limited-edition speakers. Their production will be sent to B&Ks distribution centers in other continents. More concisely, these distribution centers are located in Santiago de Chile (Chile), Atlanta (USA), Frankfurt (Germany), and Shanghai (China). The cost of producing these speakers varies with the location they are produced at. Likewise, transporting them to the companys distribution centers has a variable transportation cost that depends on the route. Production costs and capacities for the next month are given in Table 1. The amount that needs to be put in inventory in each distribution center is shown in Table 2. The transportation costs (in USD/speaker) are given in Table 3.

	Production cost (per speaker)	Capacity (in speakers)
Manchester	$100	100
Edinburgh	$75	100
Southampton	$90	80

Table 1

	Santiago	Atlanta	Frankfurt	Shanghai
Demand (tons)	80	70	60	40

Table 2

Shipping cost (per speaker)	Santiago	Atlanta	Frankfurt	Shanghai
Manchester	11	8	4	15
Edinburgh	12	9	4	12
Southampton	10	8	4	13

Table 3

1. (18pt) Problems in B&Ks procurement of raw materials has resulted in shortage of their production capacity. Consequently, their new production capacities are shown in Table 4. Formulate an LP model that can at least tell B&K how to better distribute the production they can come up with.
2. (17pt) Solve this model with Excel and interpret its solution.

	Production cost (per speaker)	Capacity (in speakers)
Manchester	$100	45
Edinburgh	$75	70
Southampton	$90	55