MHB Lowest Cost Airport-Island Ferry: Determine Optimal Route

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To minimize transportation costs for tourists traveling from the airport to the island, a balance must be struck between land and water travel. The total distance to the island is 8 miles, with 5 miles on land and 3 miles across water. Given the differing costs of $0.10 per mile for land and $0.12 per mile for water, calculations must determine the optimal split of these distances. By analyzing the cost structure, the ideal transport strategy can be established to achieve the lowest overall expense. This optimization is crucial for the local travel provider's efficiency and profitability.
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a local travel provider ferries tourists from the airport located on the shorew of the mainland to an island located 5 miles down shore and 3 miles out to the sea. transporting tourists on land costs .1 dollars/mile/person while travel across water costs .12 dollars/mile/person. determine how far tourists should be transported on land and sea so that the total cost of transportation is a minimum.
 
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kcarl said:
a local travel provider ferries tourists from the airport located on the shorew of the mainland to an island located 5 miles down shore and 3 miles out to the sea. transporting tourists on land costs .1 dollars/mile/person while travel across water costs .12 dollars/mile/person. determine how far tourists should be transported on land and sea so that the total cost of transportation is a minimum.

Start by drawing a diagram.
 
Thread 'Problem with calculating projections of curl using rotation of contour'

Thread 'Problem with calculating projections of curl using rotation of contour'

Hello! I tried to calculate projections of curl using rotation of coordinate system but I encountered with following problem. Given: ##rot_xA=\frac{\partial A_z}{\partial y}-\frac{\partial A_y}{\partial z}=0## ##rot_yA=\frac{\partial A_x}{\partial z}-\frac{\partial A_z}{\partial x}=1## ##rot_zA=\frac{\partial A_y}{\partial x}-\frac{\partial A_x}{\partial y}=0## I rotated ##yz##-plane of this coordinate system by an angle ##45## degrees about ##x##-axis and used rotation matrix to...
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