Chapter $5$

$4.$ A firm produces two different types, A and $B,$ of a commodity. The daily cost of producing $x$ units of A and $y$ units of $B$ is

$C(x,y)=0\mathrm{.}04x^2+0\mathrm{.}01xy+0\mathrm{.}01y^2+4x+2y+500$

Suppose that the firm sells all its output at a price per unit of RM$15$ for A and RM$9$ for $B.$

a$)$ Find the production levels $x$ and $y$ that maximize profit.

b$)$ Determine the maximum profit.