The problem describes a monopolist with a given total cost function $TC = Q^2 + 10Q + 100$, a marginal cost function $MC = 2Q + 10$, and a demand function $Q = 130 - P$, which leads to a marginal revenue function $MR = 130 - 2Q$. The goal is to find the profit-maximizing output level.

1. Problem Description

The problem describes a monopolist with a given total cost function $TC = Q^2 + 10Q + 100$, a marginal cost function $MC = 2Q + 10$, and a demand function $Q = 130 - P$, which leads to a marginal revenue function $MR = 130 - 2Q$. The goal is to find the profit-maximizing output level.

2. Solution Steps

To find the profit-maximizing output, we need to set marginal cost (MC) equal to marginal revenue (MR).

$MC = MR$

$2Q + 10 = 130 - 2Q$

Now, we solve for Q:

$2Q + 2Q = 130 - 10$

$4Q = 120$

$Q = \frac{120}{4}$

$Q = 30$

3. Final Answer

The profit-maximizing output is

3

0. So the answer is c. 30