UBike is a bicycle manufacturer based in Japan. Haruki, the supply chain manager at UBike is designing the manufacturing network and has selected four potential sitesTokyo, Sapporo, Fukuoka, and Sendai. The below table shows the annual fixed costs at the four locations as well as the cost of producing and shipping a bicycle to each of the four markets. Note that plants could have a capacity of either 250,000 or 500,000 units and that each open plant should have at least 60% capacity utilisation.

(A) Formulateanintegerlinearprogramming(ILP)modelforthisproblem.

(B) Developaspreadsheetmodelandsolvetheproblem offindingtheoptimallocation andsizingforUBikefactories. Comment onyourresults.

	ProductionandTransportationCosts($/unit)	Annual Demand
	Tokyo	Sapporo	Fukuoka	Sendai
Southwest	50	80	35	52	210,000
Northeast	65	35	70	40	150,000
Central	30	80	55	53	160,000
East	48	30	42	35	170,000
Annualfixedcostof 250,000	$8 million	$6 million	$7 million	$7.4 million
Annualfixedcostof 500,000	$12 million	$10 million	$11 million	$11.4 million