Question

in an oil field, as more wells are drilled each oil well pumps less oil; however, the total amount of oil pumped may increase. Suppose an oil field with 20 wells produces 10,000 barrels of oil daily. For each additional well, the production capacity of every well decrease by 10 barrels per day. Express the total volume V of oil pumped per day in terms of x, where x is the number of wells added.

Answer 1

V = (x +20)(500 -10x)

Explanation:

You want an expression for oil field volume (V) in terms of the number of wells added (x) to the 20 that are producing 10,000 bbl per day, if the volume per well decreases by 10 bbl/day for each added well.

Wells

The number of wells in the field will be (20+x).

Capacity

The volume per well with none added is (10,000 bbl)/(20 wells) = 500 bbl/well. For x added wells, that volume per well is said to be (500 -10x).

Total volume

The total volume from the field is the product of the number of wells and the capacity of each:

V = (20 +x)(500 -10x)

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Additional comment

Adding 15 wells will boost production to a maximum of 12,250 bbl/day. The last of those wells adds 10 bbl/day to the total production, so is probably not worth the cost.

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