Answer:
The amount of ovens that must be produced in a week to earn a $1610 profit is 70.
Step-by-step explanation:
Given:
A small-appliance manufacturer determines the profit P (in dollars) from producing x microwave ovens weekly by the formula:

with 0 ≤ x ≤ 200.
The target profit is $1610
So, set P = 1610, then solve for x:

Multiply both sides by 10:




Next, factor the quadratic:

Solving for x gives:

Since x=230 is outside the domain 0 ≤ x ≤ 200, we discard it.
Hence, the valid solution is x=70.
Therefore, to achieve a $1610 profit, the manufacturer must produce 70 ovens weekly.