SOLUTION: A landscape architect wished to enclose a rectangular garden on one side by a brick wall costing $20/ft and on the other three sides by a metal fence costing $10/ft. If the area of

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Question 1140031: A landscape architect wished to enclose a rectangular garden on one side by a brick wall costing $20/ft and on the other three sides by a metal fence costing $10/ft. If the area of the garden is 122 square feet, find the dimensions of the garden that minimize the cost.
Found 2 solutions by math_helper, ikleyn:
Answer by math_helper(2461)   (Show Source): You can put this solution on YOUR website!



L*W = 122                   (1)



Cost equation:

C = 20L + 10L + 10W + 10W   

C = 30L + 20W               (2)  



Eq (1) -->   L = 122/W



Substitute for L in (2):



C = 30*(122/W) + 20W

C = 3660/W + 20W



Differentiate WRT to W:

dC/dW = -(3660/W^2) + 20



Set the derivative to 0:

  -(3660/W^2) + 20 = 0

   20W^2 = 3660

     W^2 = 183

     W  =  ft



L = 122/13.52775 =  ft





[ min(C) = $541.11   for these dimensions ]



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Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
 .





The formulation of the problem is DEFECTIVE.







 

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