Develop a 2d plot for average cost versus the, Mathematics

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Develop a 2d plot for average cost versus the

Consider the demand function is and the total cost function is.

Questions

Use of MATHEMATICA (or of any other software) is recommended. Choose any of the projects and answer the question for your selected project at the end of this document.

1. Develop a 2D plot for demand versus the price.

2. Develop a 2D plot for average cost versus the quantity.

3. Compute the demand elasticity when price equal to 1.

4. Compute the marginal cost when the quantity is equal 1.

5. Develop the profit function.

6. Find the quantity that maximizes the total profit.

7. What is the price that maximizes the profit?

8. What is the maximum profit?

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