Example of the “Principle of Median Location”

“GORILLA” pasta plant:

"Gorilla Plant Location Problem"
STATE	POP1996	"rail miles"	Fargo	Sioux Falls	Milwaukee	Mpls	Ames	Omaha	Chicago	Kansas City	StLouis
North Dakota	633534	Fargo	0	160	720	160	320	320	640	480	640
South Dakota	721374	Sioux Falls	160	0	720	480	320	160	640	480	640
Wisconsin	5144123	Milwaukee	720	720	0	560	400	560	80	560	240
Minnesota	4639933	Mpls	160	480	560	0	160	320	480	320	480
Iowa	2831890	Ames	320	320	400	160	0	160	320	160	320
Nebraska	1622272	Omaha	320	160	480	320	160	0	480	320	480
Illinois	11731783	Chicago	640	640	80	480	320	480	0	480	160
Kansas	2574771	Kansas City	480	480	560	320	160	320	480	0	160
Missouri	5322268	StLouis	640	640	240	480	320	480	160	160	0
total pop:	35221948
		freight rates from P. Baumol 8/27/97:
		by rail	by truck
		Wheat	pasta	ton wheat/ton pasta is:		1.1
	$/ton/mi	$0.15	$0.38	tons pasta/person/year is:		0.025	50	lbs per year/person
		pop:	633534	721374	5144123	4639933	2831890	1622272	11731783	2574771	5322268	Annual	compared to
		Fargo	Fargo	Sioux Falls	Milwaukee	Mpls	Ames	Omaha	Chicago	Kansas City	StLouis	transport costs	AMES
	Fargo	$0	$0	$1,096,488	$35,185,801	$7,052,698	$8,608,946	$4,931,707	$71,329,241	$11,740,956	$32,359,389	$172,305,226	127%
	Sioux Falls	$23,246,486	$962,972	$0	$35,185,801	$21,158,094	$8,608,946	$2,465,853	$71,329,241	$11,740,956	$32,359,389	$207,057,738	153%
	Milwaukee	$104,609,186	$4,333,373	$4,934,198	$0	$24,684,444	$10,761,182	$8,630,487	$8,916,155	$13,697,782	$12,134,771	$192,701,577	142%
	Mpls	$23,246,486	$962,972	$3,289,465	$27,366,734	$0	$4,304,473	$4,931,707	$53,496,930	$7,827,304	$24,269,542	$149,695,613	111%
	Ames	$46,492,971	$1,925,943	$2,192,977	$19,547,667	$7,052,698	$0	$2,465,853	$35,664,620	$3,913,652	$16,179,695	$135,436,078	100%
	Omaha	$46,492,971	$1,925,943	$1,096,488	$23,457,201	$14,105,396	$4,304,473	$0	$53,496,930	$7,827,304	$24,269,542	$176,976,250	131%
	Chicago	$92,985,943	$3,851,887	$4,385,954	$3,909,533	$21,158,094	$8,608,946	$7,397,560	$0	$11,740,956	$8,089,847	$162,128,720	120%
	Kansas City	$69,739,457	$2,888,915	$3,289,465	$27,366,734	$14,105,396	$4,304,473	$4,931,707	$53,496,930	$0	$8,089,847	$188,212,926	139%
	StLouis	$92,985,943	$3,851,887	$4,385,954	$11,728,600	$21,158,094	$8,608,946	$7,397,560	$17,832,310	$3,913,652	$0	$171,862,946	127%
FACTS:
The Gorilla Pasta company wants to serve the Midwest market												$142,595,356.00
They plan on selling 50/lbs pasta/person/year in that market.					How many tons/person is that @ 2000 lbs/ton?
Pasta production technology requires 1.1 ton wheat for each ton pasta produced
The minimum efficient scale of pasta production is reached at about 2,000 tons per day							How many tons per year is that @365 days/yr?
An unlimited supply of wheat can be obtained from Fargo, North Dakota.
It costs $0.15/ton/mile to ship wheat by rail. It costs $0.38/ton/mile to ship pasta by truck.
Distances between rail stops in the Midwest, and actual data on the populations around each stop, are listed above
QUESTIONS:
How many plants should Gorilla open in the Midwest?
Where should the plant(s) be located? The criterion is:
	choose the site to minimize input transport costs					input T costs =		qi * ti * D(Fargo-site)*total mkt Q
	plus output transport costs					output T costs =		SUM(POPm* tons/person * to * Dsm)
If customers in Chicago are willing to pay twice as much per pound of pasta than all the other Midwesterners, would the optimal plant location(s) be different?
What is the difference between the annual transport costs at the SECOND best site and the best site, PER YEAR?