#### Answer

$C(x)=30x+100$

#### Work Step by Step

Assuming a linear cost function, $C(x)=mx+b$, where
m represents the marginal cost and
b represents the fixed cost.
Here,
b= $\$ 100$ (fixed cost) and
m= $?$ (the cost to produce one item).
Let $C(x)=$ cost of producing $x$ items.
$C(x)=mx+100$
We don't know m, but we were given $C($50$)=1600$ ,
so we solve (for m):
$m(50)+100=1600$
$50m=1500\qquad/\div 50$
$m=30$.
So,
$C(x)=30x+100$