Three different bacteria are cultured in one environment and feed on three nutrients. Each individual of species I consumes 1 unit of each of the first and second nutrients and 2 units of the third...

Three different bacteria are cultured in one environment and feed on three nutrients. Each individual of species I consumes 1 unit of each of the first and second nutrients and 2 units of the third nutrient. Each individual of species II consumes 2 units of the first nutrient and 2 units of the third nutrient. Each individual of species III consumes 2 units of the first nutrient, 3 units of the second nutrient, and 5 units of the third nutrient. If the culture is given 5300 units of the first nutrient, 7500 units of the second nutrient, and 12,800 units of the third nutrient, how many of each species can be supported such that all of the nutrients are consumed? (Letx = species I,y = species II, andz = species III. If there are infinitely many solutions, express your answers in terms ofz as in Example 3.)

 where 2200 ≤z ≤ 2500