A landscape architect wished to enclose a rectangular garden on one side by a brick wall costing $30/ft and on the other three sides by a metal fence costing $10/ft. If the area of the garden is 42 square feet, find the dimensions of the garden that minimize the cost.

Answer 1

Let x be the brick wall side length and y be the other dimension.
x y = 42 (area requirement)
10 (x+2y) + 30 x = Cost(x,y)
Substitute 42/x for y in the Cost equation to get an equation for cost in terms of x only.
Cost(x) = 10(x + 84/x) + 30x
= 40x + 84/x
Set the derivative equal to 0 and solve fpr x to see where the minimum cost occurs.