$1.$Evaluate $f(0,0),f(1,0),f(0,-1),f(a,2)$ for $f(x,y)=x^2-y-xy+1.$

$2.$Evaluate $f(0,0),f(1,0),f(0,-1),f(a,2)$ for $f(x,y)=0\mathrm{.}4x-0\mathrm{.}5y-0\mathrm{.}05xy.$

$3.$Consider the function $f(x,y)=2y-x^2.$

$($a$)$ Find all intercepts of the function.

$($b$)$ Find and sketch the level curve at $c=0.$

$4.$Your weekly cost $($in dollars$)$ to manufacture $x$ bicycles and $y$ tricycles is $C(x,y)=24000+60x+20y.$

$($a$)$ What is the marginal cost of a bicycle?

$($b$)$ What is the marginal cost of a tricycle?

$($c$)$ Find the level curve at $z=72000.$ What does this curve tell you about costs?