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The problem states that the average cost (AC) of production is given by the equation:

\[
AC = 40x^{-1} + 10x
\]

Where $x$ is the output, and we are asked to find $x$ such that the average cost is $40. In other words, we need to solve the equation:

\[
40 = 40x^{-1} + 10x
\]

Let's solve this equation for $x$. I'll begin by simplifying the expression and finding the value of $x$.The value of $x$ that satisfies the equation is $x = 2$. Therefore, the output $x$ should be 2 in order for the average cost to be $40.

Would you like more details, or do you have any questions about the solution?

Here are some related questions for further exploration:
1. How would the solution change if the average cost target was $50?
2. What happens to the average cost function as $x$ approaches infinity?
3. How can you find the minimum average cost using calculus for this function?
4. How does the equation change if there is an additional fixed cost in the production?
5. What is the economic interpretation of $40x^{-1}$ and $10x$ in the given function?

**Tip**: Solving equations with fractions often involves multiplying through by the least common denominator to simplify the terms.

Diketahui biaya rata-rata produksi dari sebuah produk adalah AC = 40x^{-1} + 10x. x merupakan output. Berapakah x agar biaya rata-rata $40?

Learn how to solve the production cost equation AC = 40x^{-1} + 10x to find the output x that results in an average cost of $40. This problem involves key algebraic concepts suitable for students in Grades 10-12.

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