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

1. on a 2 - hectare coconut farm with an 8m x 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 x 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 x 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 x 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 a square - shaped planting pattern, the area per tree is (A = s\times s), where (s) is the planting distance. 1 hectare = 10000 square meters. For the first farm with (s = 8m), area per tree (A_1=8\times8 = 64m^{2}). Number of trees per hectare (n_1=\frac{10000}{64}\approx156.25) trees. For a 2 - hectare farm, number of trees (N_1 = 2\times156.25=312.5) trees. For the second farm with (s = 9m), area per tree (A_2 = 9\times9=81m^{2}). Number of trees per hectare (n_2=\frac{10000}{81}\approx123.46) trees. For a 3 - hectare farm, number of trees (N_2=3\times123.46 = 370.38) trees.

Step2: Calculate fertilizer rate for the first farm (Question 1)

Total fertilizer per tree (=500 + 250+500=1250g = 1.25kg). Recommended fertilizer rate for 2 - hectare farm (=1.25\times312.5 = 390.625kg).

Step3: Calculate total fertilizer per tree for the second farm (Question 2)

Total fertilizer per tree (=600 + 800+400=1800g=1.8kg). Total fertilizer for 3 - hectare farm for one - time application (=1.8\times370.38 = 666.684kg).

Step4: Calculate fertilizer amount for each season (Question 2a)

Since the farmer splits the application into two equal doses, fertilizer amount for each season (=\frac{666.684}{2}=333.342kg).

Step5: Calculate cost of each fertilizer for one - time application

Cost of urea for one - time application: Urea amount per tree is (600g = 0.6kg), for 370.38 trees, amount of urea (=0.6\times370.38 = 222.228kg), cost of urea (=222.228\times45=$9999.26). Cost of muriate of potash for one - time application: Muriate of potash amount per tree is (800g = 0.8kg), for 370.38 trees, amount of muriate of potash (=0.8\times370.38 = 296.304kg), cost of muriate of potash (=296.304\times50=$14815.2). Cost of ammonium phosphate for one - time application: Ammonium phosphate amount per tree is (400g = 0.4kg), for 370.38 trees, amount of ammonium phosphate (=0.4\times370.38 = 148.152kg), cost of ammonium phosphate (=148.152\times55=$8148.36).

Step6: Calculate combined total for the entire season (Question 2b)

Total cost for one - time application (=9999.26+14815.2 + 8148.36=$32962.82). Combined total for the entire season (both applications) (=2\times32962.82=$65925.64)

Answer:

  1. Recommended fertilizer rate for 2 - hectare farm: (390.625kg)
  2. a. Fertilizer amount for each season: (333.342kg) b. Combined total for the entire season: ($65925.64)