Assume that a competitive firm has the total cost function:

TC=1q3−40q2+890q+1800

Suppose the price of the firm's output (sold in integer units) is $600 per unit.

Create tables (but do not use calculus) with columns representing cost, revenue, and profit to find a solution.

How many units should the firm produce to maximize profit?

Please specify your answer as an integer.

What is the total profit at the optimal output level?

Please specify your answer as an integer.

To find the number of units the firm should produce to maximize profit, we will calculate the total cost (TC), total revenue (TR), and profit (π) for various quantities of output, and then find where profit is maximized.

The given total cost (TC) function is:

\[
TC(q) = q^3 - 40q^2 + 890q + 1800
\]

The price per unit of output is $600, so the total revenue (TR) is:

\[
TR(q) = 600q
\]

The profit (π) is:

\[
\pi(q) = TR(q) - TC(q) = 600q - (q^3 - 40q^2 + 890q + 1800)
\]

We will now create a table for values of $ q $, calculating TC, TR, and $ \pi $ (profit). I'll test for integer values of $ q $, and then find the output level that maximizes profit.

Let me calculate this.Based on the table and calculations, the firm maximizes profit at a production level of **22 units**.

The total profit at the optimal output level of 22 units is **$532**.

Would you like further details or explanations?

Here are 5 related questions you might find interesting:
1. How do changes in the price per unit affect the optimal production level?
2. What happens to profit if fixed costs in the total cost function increase?
3. How would introducing marginal cost analysis alter the strategy for maximizing profit?
4. Can you calculate the marginal profit per unit produced?
5. How sensitive is the optimal production level to small changes in the total cost function?

**Tip:** In competitive markets, firms maximize profit by producing the quantity where marginal cost equals marginal revenue (MC = MR).

Assume that a competitive firm has the total cost function: TC = q^3 - 40q^2 + 890q + 1800. Suppose the price of the firm's output (sold in integer units) is $600 per unit. Create tables (but do not use calculus) with columns representing cost, revenue, and profit to find a solution. How many units should the firm produce to maximize profit? Please specify your answer as an integer. What is the total profit at the optimal output level? Please specify your answer as an integer.

Explore how to determine the optimal production level for a competitive firm using cost, revenue, and profit analysis without calculus. Learn to calculate total cost (TC), total revenue (TR), and profit (π) to find the production level that maximizes profit. Suitable for students in Grades 11-12 or undergraduate economics courses.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation