$C=32\sqrt[\phantom{2}]{xy}+165x+220y+1,050.$

$(a)$ Find the marginal costs and $\{$:$\frac{\text{d}\text{e}\text{l}\text{C}}{\text{d}\text{e}\text{l}\text{y}})$ when $x=80$ and $y=20.$

$C_x(80,20)=$

$C_y(80,20)=220$

$(b)$ When additional production $is$ required, which model $of$ stove results $in$ the cost increasing $at$ a higher rate? How can this $be$ determined from the cost model?

When additional production $is$ required, the cost $of$ the stove $is$ increasing $at$ a higher rate because $\frac{\text{d}\text{e}\text{l}\text{C}}{\text{d}\text{e}\text{l}\text{y}}$

$\frac{\text{d}\text{e}\text{l}\text{C}}{\text{d}\text{e}\text{l}\text{x}}.$