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Tunnel problem

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In the summer of 1999, construction will begin on a 3000 ft. tunnel that will pass under the Mississippi River, connecting the cities of East St. Louis, Illinois and St. Louis, Missouri. A Missouri-based company has been contracted to begin excavating the tunnel from the Missouri side, while an Illinois-based company will begin from the Illinois side.

The cost of digging the tunnel depends on many factors, including the overall length of the tunnel. However, the cost per unit length is not constant: as the tunnel gets longer, the cost per unit length increases because of the increasing expense of carrying tools and workers in and hauling dirt and rock out. In their initial bids, both companies have suggested that their rates per foot vary linearly with distance. Their rates are summarized in the following table:

Distance-ft:250 750 1250 1750 2250 2750

Cost per foot ($)
IL Company 995 2945 4895 6845 8795 10745
MO Company 725 2775 4825 6875 8925 10975

For each company, determine a function that gives that cost of digging x feet of tunnel (NOT the cost per foot as a function of distance dug).

***If my chart is hard to see, it's also here http://faculty.prairiestate.edu/skifowit/htdocs/projects/a07.htm Problem #2

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Solution Summary

This shows how to write a function for a given situation involving digging a tunnel.

Solution provided by:
  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
Recent Feedback
  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
  • "excellent work"
  • "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
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  • "Thank you very much for your valuable time and assistance!"
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