I believe, that mathematically there is infinite number of solutions. I suppose the values of goods are supposed to be a whole number, since I was unable to find a solution with natural numbers as values of goods in the interval of solutions <-1000; 1000>.
If the solution is supposed to be a natural number, I found:
75 (meat = 4; patries = -5; food = 4; flour = 5)
459 (meat = -38; patries = -8; food = 38; flour = 19)
843 (meat = -80; patries = -11; food = 72; flour = 33)
If the solution is supposed to be a whole number, I also found:
-309 (meat = 46; patries = -2; food = -30; flour = -9)
-693 (meat = 88; patries = 1; food = -64; flour = -23)
There are some wannabes:
651 (meat = -59; patries = -9,5; food = 55; flour = 26)
-501 ((meat = 67; patries = -0,5; food = -47; flour = -16)
-885 (meat = 109; patries = 2,5; food = -81; flour = -30)
And a lot more kinda pretty numbers:
555; 747; 795; 939; -405; -789; -981
Hope I didnt mistype. Anyway thx for some brainteaser.
Standouch (CZ101 Golden Gate)