Problem linear programmin

[Guest]

Andrea has just received an inheritance of land of 10,000 m2 and three jobs must be carried out on it, continue with the cultivation of two types of oranges (Navel and Navelate), two types of tomatoes (cherry and Roma) and repopulate the area near the source of water with guava and Moringa. The utilities generated by each square meter of oranges are 3 and 52/ dollars respectively; for the cultivation of tomatoes it is about 7/2 and 4 dollars respectively, and by the depopulation $ 5. As a rule, at least 40% of the land must be used in orange growing and at most 35% in tomatoes or repopulation. Determine how the land should be distributed to obtain the maximum benefit.

[HallsofIvy]

The problem says "three jobs" but there are 6 values you want to find: A, the number of square meters devoted to navel oranges; B, the number of square meters devoted to navelate oranges, C, the number of square meters devoted to cherry tomatoes; D, the number of square meters devoted to roma tomatoes; E, the number of square meters devoted to guavas; and F, the number of square meters devoted to Moringas.

You have a total or 10000 square meters so [tex]A+ B+ C+ D+ E+ F\le 10000[/tex].
"As a rule, at least 40% of the land must be used in orange growing and at most 35% in tomatoes or repopulation:
so [tex]A+ B\ge 4000[/tex] and [tex]C+ D+ E+ F\le 3500[/tex].

The objective, to be maximized, is 3A+ 52B+ 7C/2+ 4D+ 5E+ 5F.