Three neighbours buy a piece of land that they want to cultivate as a garden. The land has the shape of a square. To avoid that their petunias and pumpkins get in the way of each other, they decide to split the garden into three cells of equal area. To keep things simple, the border between two adjacent cells should be a straight line. Under these constraints, can you help them to divide their garden such that the total length of the fence is minimized? How would you divide the garden for five, six, seven or eight neighbours?

this seems to be an optimazation problem where a constraint equation is necessary and the surface area of the plot of land ( amt of total fencing) needs to be minimized namely through differentiation.

Perhaps you could say A=xy

min s(a)= 2x + 4y

substituting s(a)= 2x + 4A/x

the next step would be to take a derivative and see if there is indeed a minimum however a value for A ( area of the land) is not given to us so

Posted by alex on 2007-08-19 00:49:30