anonymous
  • anonymous
Applied Calc - An underground electricity cable is to be laid between two boat docks on opposite banks of a river. One boat dock is 600 feet downstream from the other. The river is 200 feet wide. If the cost of laying the cable is $50 per foot under water and $30 per foot on land, how should the cable be laid to minimize the cost to connect the two docks? Also, find the minimum cost to lay such a cable.
Mathematics
  • Stacey Warren - Expert brainly.com
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
|dw:1332954978326:dw|So we can either do a direct path (all underwater) from 1 dock to the other, or a mixture of land cable and underwater cable to connect the two. Calling l the length of land cable and w the length of underwater cable, the total cost can be expressed as: C=30l+50w
anonymous
  • anonymous
We need to related l and w with each other. The geometry of they problem makes this possible. |dw:1332955488825:dw|
anonymous
  • anonymous
So,\[w=\sqrt[]{(600-l)^2+200^2}\]And our cost as a function of l alone is: \[C(l)=30l+50\sqrt{(600-l)^2+200^2}\]We need to minimize this with respect to l.

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