Applications of Differentiation: Optimization Problem

[Tgleaso1]

A farmer wishes to enclose a rectangular pen with area 100 squarefeet next to a road. The fence along the road is to be reinforced and costs $34per foot. Fencing that costs $16 per foot can be used for the other threesides. What dimensions for the pen will minimize the cost to the farmer?

 

[Unknown008]

Hm... not quite.

You need to work in terms of cost, not directly in terms of the sides.

Cost for the 3 sides = (2y + x)16
Cost for the last side = 34x

Total cost = 16(2y+x) + 34x

This is what you differentiate. Replace y by something in terms of x that you already know, then solve for x. I'm sure you'll get something lower than $820