maximize  5a_1,M,C + 6a_1,M,F + 5.5a_1,M,I + 7a_1,M,P + 5.5a_1,M,L +
	6a_2,M,C + 7.5a_2,M,F + 6.75a_2,M,I + 8.25a_2,M,P + 6a_2,M,L + 
 	4b_1,M,C + 8b_1,M,F + 7b_1,M,I + 8b_1,M,P + 7b_1,M,L +
	7b_2,M,C + 9b_2,M,F + 7.5b_2,M,I + 8b_2,M,P + 9b_2,M,L +
	8b_3,M,C + 10b_3,M,F + 10b_3,M,I + 9b_3,M,P + 11b_3,M,L +
	5a_1,E,C + 6a_1,E,F + 5.5a_1,E,I + 7a_1,E,P + 5.5a_1,E,L +
	6a_2,E,C + 10a_2,E,F + 6.75a_2,E,I + 11a_2,E,P + 5.5a_2,E,L +
	11b_1,E,C + 15b_1,E,F + 13b_1,E,I + 15b_1,E,P + 12b_1,E,L +
	10b_2,E,C + 13b_2,E,F + 12b_2,E,I + 13.50b_2,E,P + 11b_2,E,L +
	9b_3,E,C + 13b_3,E,F + 12.50b_3,E,I + 14b_3,E,P + 10.50b_3,E,L +
	15a_1,W,C + 8a_1,W,F + 9a_1,W,I + 8a_1,W,P + 10a_1,W,L +
	13a_2,W,C + 10a_2,W,F + 11a_2,W,I + 9.50a_2,W,P + 11.75a_2,W,L 
!aluminum example from lecture 9-27-99
!variables:
!a_1,W,C=amount of A1 produced in West factory and shipped to California
subject to
!demand constraints
demCA1) a_1,E,C + a_1,W,C + a_1,M,C = 250 !California product A1 demand
demCA2) a_2,E,C + a_2,W,C + a_2,M,C = 150 !California product A2 demand
demCB1) b_1,E,C + b_1,M,C = 200 !California product B1 demand
demCB2) b_2,E,C + b_2,M,C = 250 !California product B2 demand
demCB3) b_3,E,C + b_3,M,C = 200 !California product B3 demand
dem_FA1) a_1,E,F + a_1,W,F + a_1,M,F = 150 !Florida product A1 demand
dem_FA2) a_2,E,F + a_2,W,F + a_2,M,F = 100 !Florida product A2 demand
dem_FB1) b_1,E,F + b_1,M,F = 200 !Florida product B1 demand
dem_FB2) b_2,E,F + b_2,M,F = 250 !Florida product B2 demand
dem_FB3) b_3,E,F + b_3,M,F = 200 !Florida product B3 demand
dem_IA1) a_1,E,I + a_1,W,I + a_1,M,I = 300 !Illinois product A1 demand
dem_IA2) a_2,E,I + a_2,W,I + a_2,M,I = 325 !Illinois product A2 demand
dem_IB1) b_1,E,I + b_1,M,I = 125 !Illinois product B1 demand
dem_IB2) b_2,E,I + b_2,M,I = 100 !Illinois product B2 demand
dem_IB3) b_3,E,I + b_3,M,I = 75 !Illinois product B3 demand
dem_PA1) a_1,E,P + a_1,W,P + a_1,M,P = 80 !Pennsylvania product A1 demand
dem_PA2) a_2,E,P + a_2,W,P + a_2,M,P = 100 !Pennsylvania product A2 demand
dem_PB1) b_1,E,P + b_1,M,P = 125 !Pennsylvania product B1 demand
dem_PB2) b_2,E,P + b_2,M,P = 45 !Pennsylvania product B2 demand
dem_PB3) b_3,E,P + b_3,M,P = 200 !Pennsylvania product B3 demand
dem_LA1) a_1,E,L + a_1,W,L + a_1,M,L = 115 !Louisiana product A1 demand
dem_LA2) a_2,E,L + a_2,W,L + a_2,M,L = 125 !Louisiana product A2 demand
dem_LB1) b_1,E,L + b_1,M,L = 55 !Louisiana product B1 demand
dem_LB2) b_2,E,L + b_2,M,L = 45 !Louisiana product B2 demand
dem_LB3) b_3,E,L + b_3,M,L = 65 !Louisiana product B3 demand
!Processing time constraints
!primary equipment processing time constraint for the East factory
ptime_E) 0.25a_1,E,C + 0.25a_1,E,F + 0.25a_1,E,I + 0.25a_1,E,P 
+ 0.25a_1,E,L +
	0.15a_2,E,C + 0.15a_2,E,F + 0.15a_2,E,I 
+ 0.15a_2,E,P + 0.15a_2,E,L +
	0.1b_1,E,C + 0.1b_1,E,F + 0.1b_1,E,I + 0.1b_1,E,P + 0.1b_1,E,L +
	0.15b_2,E,C + 0.15b_2,E,F + 0.15b_2,E,I + 0.15b_2,E,P + 0.15b_2,E,L 
+0.2b_3,E,C + 0.2b_3,E,F + 0.2b_3,E,I + 0.2b_3,E,P + b_3,E,L < 600
!primary equipment processing time constraint for the West factory
ptime_W) 0.15a_1,W,C + 0.15a_1,W,F + 0.15a_1,W,I + 0.15a_1,W,P + 0.15a_1,W,L 
+0.05a_2,W,C + 0.05a_2,W,F + 0.05a_2,W,I + 0.05a_2,W,P + 0.05a_2,W,L < 200
!primary equipment processing time constraint for the MidAtlantic factory
ptime_M) 0.2a_1,M,C + 0.2a_1,M,F + 0.2a_1,M,I + 0.2a_1,M,P + 0.2a_1,M,L +
	0.15a_2,M,C + 0.15a_2,M,F + 0.15a_2,M,I + 0.15a_2,M,P + 0.15a_2,M,L +
	0.1b_1,M,C + 0.1b_1,M,F + 0.1b_1,M,I + 0.1b_1,M,P + 0.1b_1,M,L +
	0.2b_2,M,C + 0.2b_2,M,F + 0.2b_2,M,I + 0.2b_2,M,P + 0.2b_2,M,L +
	0.22b_3,M,C + 0.22b_3,M,F + 0.22b_3,M,I + 0.22b_3,M,P + 0.22b_3,M,L 
< 195
!secondary equipment processing time constraint for the East factory
	stime_E) 1.2b_1,E,C + 1.2b_1,E,F + 1.2b_1,E,I + 1.2b_1,E,P 
+ 1.2b_1,E,L +
	1.25b_2,E,C + 1.25b_2,E,F + 1.25b_2,E,I + 1.25b_2,E,P + 1.25b_2,E,L +
	2b_3,E,C + 2b_3,E,F + 2b_3,E,I + 2b_3,E,P + b_3,E,L < 1500
!secondary equipment processing time constraint for the MidAtlantic factory
stime_M) b_1,M,C + b_1,M,F + b_1,M,I + b_1,M,P + b_1,M,L +
	1.4b_2,M,C + 1.4b_2,M,F + 1.4b_2,M,I + 1.4b_2,M,P + 1.4b_2,M,L +
	1.9b_3,M,C + 1.9b_3,M,F + 1.9b_3,M,I + 1.9b_3,M,P + 1.9b_3,M,L < 4995
!Facility constraints
!East facility constraint
fac_E) a_1,E,C + a_1,E,F + a_1,E,I + a_1,E,P + a_1,E,L +
	a_2,E,C + a_2,E,F + a_2,E,I + a_2,E,P + a_2,E,L +
	b_1,E,C + b_1,E,F + b_1,E,I + b_1,E,P + b_1,E,L +
	b_2,E,C + b_2,E,F + b_2,E,I + b_2,E,P + b_2,E,L +
	b_3,E,C + b_3,E,F + b_3,E,I + b_3,E,P + b_3,E,L < 2000
!West facility constraint
fac_W) a_1,W,C + a_1,W,F + a_1,W,I + a_1,W,P + a_1,W,L +
	a_2,W,C + a_2,W,F + a_2,W,I + a_2,W,P + a_2,W,L < 1000
!MidAtlantic facility constraint
fac_M) a_1,M,C + a_1,M,F + a_1,M,I + a_1,M,P + a_1,M,L +
	a_2,M,C + a_2,M,F + a_2,M,I + a_2,M,P + a_2,M,L +
	b_1,M,C + b_1,M,F + b_1,M,I + b_1,M,P + b_1,M,L +
	b_2,M,C + b_2,M,F + b_2,M,I + b_2,M,P + b_2,M,L +
	b_3,M,C + b_3,M,F + b_3,M,I + b_3,M,P + b_3,M,L < 925
end