https://file.aiquickdraw.com/mathbot/file/1727986070030ahirboq6.jpg

Let's analyze and solve the given problem. The cost function provided is:

\[
C(x) = 220 + 700x + x^2
\]

where \( C(x) \) represents the total cost to produce \( x \) items. 

The questions require us to:

**a)** Find the average cost at the production level \( x = 1350 \).

The average cost function is given by:

\[
\text{Average Cost} = \frac{C(x)}{x} = \frac{220 + 700x + x^2}{x}
\]

For \( x = 1350 \), substitute this value into the equation to compute the average cost.

**b)** Find the production level \( x \) that minimizes the average cost.

This requires finding the critical points of the average cost function, which involves taking its derivative, setting it equal to zero, and solving for \( x \).

**c)** Find the minimal average cost.

Substitute the \( x \)-value from part (b) into the average cost function to compute the minimal average cost.

Would you like a detailed solution for each part now?

Below, C(x) is the cost, in dollars, to produce x items in a factory. Find the following: (a) The average cost at the production level 1350, (b) The production level that will minimize the average cost, and (c) The minimal average cost.

Learn how to calculate the average cost and minimize it for a quadratic cost function C(x) = 220 + 700x + x^2. This step-by-step guide walks through finding the average cost at production level 1350 and determining the production level that minimizes the average cost.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation