set products := { "prod1" , "prod2" , "prod3" , "prod4" , "prod5" , "prod6" , "prod7" };
set months := {1, 2, 3, 4, 5, 6};
set months_zero := {0, 1, 2, 3, 4, 5, 6};
set tools := { "szlifierka", "wiertarka_pion", "wiertarka_poziom", "swider", "strugarka" };
param profit[products] := <"prod1"> 10, <"prod2"> 6, <"prod3"> 8, <"prod4"> 4, <"prod5"> 11, <"prod6"> 9, <"prod7"> 3;

param time_needed[tools * products] :=
						|"prod1", "prod2", "prod3", "prod4", "prod5", "prod6", "prod7"|
|"szlifierka"			|   0.5 ,    0.7 ,      0 ,      0 ,    0.3 ,    0.2 ,    0.5 |
|"wiertarka_pion"		|   0.1 ,    0.2 ,      0 ,    0.3 ,      0 ,    0.6 ,      0 |
|"wiertarka_poziom"     |   0.2 ,      0 ,    0.8 ,      0 ,      0 ,      0 ,    0.6 |
|"swider"          		|  0.05 ,   0.03 ,      0 ,   0.07 ,    0.1 ,      0 ,   0.08 |
|"strugarka"            |     0 ,      0 ,   0.01 ,      0 ,   0.05 ,      0 ,   0.05 |;

param machine_available_hour[tools * months] :=
						| 1		, 2 	, 3 	, 4 	, 5 	, 6 	|
|"szlifierka"			| 1152	, 1536 	, 1536	, 1536 	, 1152 	, 1536  |
|"wiertarka_pion"		|  768	,  768 	,  768 	,  384 	,  384 	,  768 	|
|"wiertarka_poziom"		| 1152	,  384 	, 1152 	, 1152 	, 1152 	,  768 	|
|"swider"				|  384	,  384 	,    0 	,  384 	,  384 	,  384 	|
|"strugarka"			|  384	,  384 	,  384 	,  384 	,  384 	,    0 	|;


param sales[months * products] :=
	| "prod1" 	, "prod2" 	, "prod3" 	, "prod4" 	, "prod5" 	, "prod6" 	, "prod7" |
| 1	| 500		, 1000 		, 300 		, 300 		, 800 		, 200 		, 100 	  |
| 2	| 600		, 500		, 200		, 0 		, 400 		, 300 		, 150	  |
| 3	| 300		, 600		, 0 		, 0 		, 500 		, 400		, 100 	  |
| 4	| 200		, 300 		, 400 		, 500 		, 200 		, 0 		, 100 	  |
| 5	| 0			, 100		, 500 		, 100		, 1000 		, 300		, 0 	  |
| 6	| 500		, 500		, 100 		, 300		, 1100 		, 500		, 60 	  |;


#sprzedaz
var sold[products * months] >= 0;
#produkcja
var production[products * months] integer >= 0;
#magazyn
var magazine[products * months_zero] >= 0;


maximize earnings:
	sum<a, b> in products * months: (sold[a, b] * profit[a] - magazine[a, b] * 0.5);


subto products_in_magazine:
	forall<a, b> in products * months: magazine[a, b] <= 100;

subto products_in_magazine_0:
	forall<a> in products: magazine[a, 0] == 0;

subto products_in_magazine_6:
	forall<a> in products: magazine[a, 6] == 50;

subto products_in_magazine_months:
	forall<a, b> in products * months: magazine[a, b] == production[a, b] - sold[a, b] + magazine[a, b-1];

subto average_machine:
	forall <a, b> in tools * months:
		sum<c> in products: time_needed[a, c] * production[c, b] <= machine_available_hour[a, b];

subto sold_all:
	forall<a, b> in products * months: sold[a, b] <= sales[b, a];