In the fruit company where you work, you are in charge of applying a growth regulator to 78 hectares of grape varieties for fresh consumption and export. The planting distances of the vines are 3m. × 3m. and previous records indicate that the improvement per hectare is 800 liters on average. There is an applicator equipment consisting of a nebulizer, whose pond has a capacity of 1500 liters. The growth regulator to be used comes in a product whose active ingredient is 52% p/v The dose of the commercial product recommended on the label is 5 liters per 100 liters of water. To enhance the effect of the application, an adjuvant will be added whose commercial product must be applied in a dose of 15cc per 100 liters of water. Amount of commercial product applied per hectare?

To determine the amount of commercial product applied per hectare, we need to calculate the total amount of water and the total amount of active ingredient required for 78 hectares.

First, let's calculate the total amount of water required for 78 hectares. Since the planting distance is 3m x 3m, there are 1111.11 vines per hectare (since 10000 sq meters = 1 hectare). Each vine requires 5 liters of water, so the total water required per hectare is:
$$\text{Water per hectare} = 1111.11 \times 5 = 5555.55 \, \text{liters}.$$

Next, let's calculate the total amount of active ingredient required for 78 hectares. The recommended dose is 5 liters of commercial product per 100 liters of water, and the commercial product has an active ingredient concentration of 52% p/v. So the amount of active ingredient in the recommended dose is:
$$\text{Active ingredient per recommended dose} = \frac{5 \, \text{liters}}{100 \, \text{liters}} \times 52\% \, \text{(p/v)} = 2.6\% \, \text{(p/v)}.$$

To calculate the total amount of active ingredient required for 78 hectares, we multiply the amount of active ingredient per recommended dose by the total water required per hectare:
$$\text{Active ingredient per hectare} = \text{Active ingredient per recommended dose} \times \text{Water per hectare} = 2.6\% \times 5555.55 \, \text{liters} = 144.44 \, \text{liters}.$$

Therefore, the amount of commercial product applied per hectare is 144.44 liters.