A company operates 16 oil wells in a designated area. Each pump, on average, extracts 240 barrels of oil daily. The company can add more wells but every added well reduces the average daily ouput of each of the wells by 8 barrels.

How many wells should the company add in order to maximize daily production?

My first attempt gives 7 extra wells, giving a total of 4232 barrels, but I haven't checked it yet!

ReplyDeleteI'm going to give the url when answer time comes, it goes into it in detail, better than my explanation.

DeleteI also get 7 - output 4232, adding 8 drops it to 4224. But I expect there is a catch because James has a devious mind*. In any case appeasing the greenies is more important that extracting poisonous fossil fuels so I suggest they should should close all of them and bask in their sense of helping save the planet.

ReplyDelete* This is a complement

https://study.com/academy/answer/a-company-operates-16-oil-wells-in-a-designated-area-each-pump-on-average-extracts-240-barrels-of-oil-daily-the-company-can-add-more-wells-but-every-added-well-reduces-the-average-daily-ouput-of-each-of-the-wells-by-8-barrels-how-many-wells-should-th.html

ReplyDelete'Well' done, chaps. ðŸ˜Ž

The solution shows it was set by a mathematician - or that I've spent too long using spreadsheets! My approach was to calculate (iterate?) the numbers from the start until a peak occured. I don't know if that's a sad commentary on me or the way the world is going!

ReplyDeleteMany thanks for a good exercise, I've been trying to repair a laptop all afternoon and it made a pleasant change!

Ian J

By my logic it's basically - being very explicit with brackets to prevent confusion -

ReplyDelete(16+E ) x (240 - (8 x E) ) = Total output

Someone else can reorganise it to solve for E (E=extra wells)

Perhaps it's (16+E) x (240 - (8 x (16+E)), as all the wells, including the original 16, lose 8 per extra well. NB: this doesn't work for E = 0

ReplyDelete