Question $15[8$ points$]$

A farmer wants to construct a fence around a rectangular field. Sides with neighbours need reinforced fencing that costs $\backslash (\backslash$$ $10\backslash )$ per meter. The other sides use regular fencing that costs $\backslash (\backslash$$ $3\backslash )$ per meter. Assuming the farmer has a neighbour on the north side, answer the following questions. Give your answers as exact expressions or decimals accurate to at least two places.

N

a$)$ Given a budget of $\backslash (\backslash$$ $500\backslash ),$ find the dimensions that give the maximum area inside the fencing.

Length of east and west fences:

Length of north and south fences:

Worksheet

m

b$)$ Find the dimensions that will cost the least to build a fence with an area of $\backslash (1956\backslash$mathrm$\{$~m$\}^\{2\}\backslash ).$

Length of east and west fences: