Answer:
The additional wells for maximum amount of oil per day is 3 wells.
Step-by-step explanation:
Given;
initial number of wells, n = 6
total production, T = 1800
average production per well, = 1800/6 = 300 barrels per day
Let the additional well = y
total number of wells after optimization = 6 + y
new production per well = 300 - 25y
new total production = (6+y)(300-25y)
t = 1800 - 150y + 300y - 25y²
t = 1800 + 150y - 25y²
dt / dy = 150 -50y
for maximum value, dt/dy = 0
150 - 50y = 0
50y = 150
y = 150 / 50
y = 3
Therefore, the additional wells for maximum amount of oil per day is 3 wells.
33 additional wells should be drilled, reaching 39 wells, to obtain the maximum amount of oil per day.
Given that an oilfield contains 6 wells that produce a total of 1,800 barrels of oil per day, and for each additional well that is drilled, the average production per well decreases by 25 barrels per day, to determine how many additional wells should be drilled to to obtain the maximum amount of oil per day, the following calculation must be performed:
Therefore, 33 additional wells should be drilled, reaching 39 wells, to obtain the maximum amount of oil per day.
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