A property owner wants to fence a garden plot adjacent to a road. The fencing next to the road must be sturdier and costs $5 per foot, but the other fencing costs just $3 per foot. The garden is to have an area of 1200 ft2. (a) Find a function that models the cost of fencing the garden.(b) Find the garden dimensions that minimize the cost of fencing.(c) If the owner has at most $600 to spend on fencing, find the range of lengths he can fence along the road.

Question

A property owner wants to fence a garden plot adjacent to a road. The fencing next to the road must be sturdier and costs $5 per foot, but the other fencing costs just $3 per foot. The garden is to have an area of 1200 ft2.

(a) Find a function that models the cost of fencing the garden.
(b) Find the garden dimensions that minimize the cost of fencing.
(c) If the owner has at most $600 to spend on fencing, find the range of lengths he can fence along the road.

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Tagged in
Math
Calculus

Applications of Derivative