1. on a 2 - hectare coconut farm with an 8m×8m planting distance, the fertilizer requirements per tree are…

1. on a 2 - hectare coconut farm with an 8m×8m planting distance, the fertilizer requirements per tree are 500 g of complete fertilizer (20 - 20 - 20), 250 g of ammonium phosphate, and 500 g of muriate of potash. calculate the recommended fertilizer rate.\n2. a 3 - hectare coconut farm with a planting distance of 9m×9m has soil deficient in nitrogen and potassium. the recommended fertilizer application per tree is as follows: urea (46 - 0 - 0): 600 grams, muriate of potash (0 - 0 - 60): 800 grams, ammonium phosphate (16 - 20 - 0): 400 grams. however, the farmer decides to split the fertilizer application into two equal doses: one at the beginning of the rainy season and another at mid - season.\n a. calculate the total amount of fertilizer needed for each season.\n b. compute the combined total for the entire season (both applications). if urea costs 45.00/kg, muriate of potash 50.00/kg, and ammonium phosphate 55.00kg.

1. on a 2 - hectare coconut farm with an 8m×8m planting distance, the fertilizer requirements per tree are 500 g of complete fertilizer (20 - 20 - 20), 250 g of ammonium phosphate, and 500 g of muriate of potash. calculate the recommended fertilizer rate.\n2. a 3 - hectare coconut farm with a planting distance of 9m×9m has soil deficient in nitrogen and potassium. the recommended fertilizer application per tree is as follows: urea (46 - 0 - 0): 600 grams, muriate of potash (0 - 0 - 60): 800 grams, ammonium phosphate (16 - 20 - 0): 400 grams. however, the farmer decides to split the fertilizer application into two equal doses: one at the beginning of the rainy season and another at mid - season.\n a. calculate the total amount of fertilizer needed for each season.\n b. compute the combined total for the entire season (both applications). if urea costs 45.00/kg, muriate of potash 50.00/kg, and ammonium phosphate 55.00kg.

Answer

Explanation:

Step1: Calculate number of trees per hectare for first farm

For an (8m\times8m) planting - distance, area per tree (A = 8\times8=64m^{2}). Since 1 hectare ( = 10000m^{2}), number of trees per hectare (n_1=\frac{10000}{64}). For a 2 - hectare farm, number of trees (N_1 = 2\times\frac{10000}{64}=\frac{20000}{64}=312.5).

Step2: Calculate total fertilizer requirements for first farm

Fertilizer per tree: 500 g of complete fertilizer (20 - 20 - 20), 250 g of ammonium phosphate, and 500 g of Muriate of potash. Total fertilizer per tree (=500 + 250+500=1250g = 1.25kg). Total fertilizer for 2 - hectare farm (=312.5\times1.25 = 390.625kg). The recommended fertilizer rate is (\frac{390.625}{2}=195.3125kg) per hectare.

Step3: Calculate number of trees per hectare for second farm

For a (9m\times9m) planting - distance, area per tree (A'=9\times9 = 81m^{2}). Number of trees per hectare (n_2=\frac{10000}{81}). For a 3 - hectare farm, number of trees (N_2=3\times\frac{10000}{81}=\frac{30000}{81}\approx370.37).

Step4: Calculate amount of each fertilizer per tree for second farm per season

Urea: 600 g per tree, so per season (=300g = 0.3kg). Muriate of Potash: 800 g per tree, so per season (=400g = 0.4kg). Ammonium Phosphate: 400 g per tree, so per season (=200g = 0.2kg).

Step5: Calculate total amount of fertilizer per season for second farm

Total fertilizer per tree per season (=0.3 + 0.4+0.2=0.9kg). Total for the 3 - hectare farm per season (=370.37\times0.9 = 333.333kg).

Step6: Calculate combined total for the entire season for second farm

Combined total for the entire season (both applications) (=370.37\times(0.3 + 0.4+0.2)\times2=666.666kg).

Step7: Calculate cost for second - farm fertilizers

Cost of Urea per tree for the season (=0.6\times45 = 27) pesos. Cost of Muriate of Potash per tree for the season (=0.8\times50 = 40) pesos. Cost of Ammonium Phosphate per tree for the season (=0.4\times55 = 22) pesos. Total cost per tree for the season (=27 + 40+22 = 89) pesos. Total cost for the 3 - hectare farm for the season (=370.37\times89=32962.93) pesos.

Answer:

  1. Recommended fertilizer rate for 2 - hectare farm: (195.3125kg) per hectare.
  2. a. Total amount of fertilizer needed for each season for 3 - hectare farm: (333.333kg). b. Combined total for the entire season for 3 - hectare farm: (666.666kg).