A property owner wants to fence a garden pot 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 square feet. Find a function that models the cost of fencing the garden, and use this function to find the garden dimensions that minimizes the cost of fencing.

Question

anonymous · Answer

put the part next to the road as x, and the adjacent side as y as in the picture.  then you know that 
$$x|dw:1320368335350:dw|y=1200$$ meaning 
$$y=\frac{1200}{x}$$

anonymous · Answer

meant 
$$xy=1200$$, 
$$y=\frac{1200}{x}$$

anonymous · Answer

cost is 
$$C(x)=5x+3x+3\times \frac{1200}{x}+3\times \frac{1200}{x}=8x+\frac{7200}{x}$$ that is what you want to minimize

anonymous · Answer

take the derivative, set it equal zero to find the critical points, solve for x and you are done