An oilfield contains 6 wells that produce a total of 1,800 barrels of oil per day. For each additional well that is drilled, the average production per well decreases by 25 barrels per day. Required:
How many additional wells should be drilled to obtain the maximum amount of oil per day?
Answers
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.
Final answer:
By setting up the equation of the total daily oil production and finding its maximum, we learn that approximately 13 additional wells should be drilled to maximize the daily oil production.
Explanation:
To find out how many additional wells should be drilled to obtain the maximum
amount of oil
per day, we must firstly set up an equation to represent the situation. The total daily oil production is equal to the number of wells multiplied by the daily production per well. Given the conditions in the question, we can express this as:
Total daily oil production = (6 + x) * (1800 - 25x)
where x represents the number of additional wells that should be drilled. In order to find the maximum of this function, we would have to differentiate this equation and set the derivative equal to 0 then solve for x. This would be up to the individual's level of mathematical experience. However, one can use a financial calculator or a graphic calculator to find the maximum and get approximately 13 additional wells.
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There's no questions or worksheet attached.
Final answer:
This question pertains to linear equations, a topic in high school level algebra. Linear equations produce a straight line when graphed and can be solved using algebraic methods. Completing the homework might involve solving for variables, graphing the equations, or interpreting the graphs.
Explanation:
The subject of this question is about Unit 4 Linear Equations Homework 12 which falls within the scope of Mathematics, specifically in the field of algebra. A linear equation is an equation between two variables that produces a straight line when graphed out. Solving such equations involves procedures such as simplification, addition, subtraction, multiplication and division.
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Step-by-step explanation:
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Answers
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Step-by-step explanation:
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For this case we want to test if the the average monthly income of all students at college is at least $2000. Since the alternative hypothesis can't have an equal sign thne the correct system of hypothesis for this case are:
Null hypothesis (H0):
Alternative hypothesis (H1):
And in order to test this hypothesis we can use a one sample t or z test in order to verify if the true mean is at least 200 or no
Step-by-step explanation:
For this case we want to test if the the average monthly income of all students at college is at least $2000. Since the alternative hypothesis can't have an equal sign thne the correct system of hypothesis for this case are:
Null hypothesis (H0):
Alternative hypothesis (H1):
And in order to test this hypothesis we can use a one sample t or z test in order to verify if the true mean is at least 2000 or no