A company has operating costs of $2000 per thousand items produced. Its revenue function can be modeled by the equation: R(x)=30x/(x+2)² , where x is measured in thousands of items produced, and C and R are measured in thousands of dollars (so C(x)=2).
1. Determine the price-demand equation, solved for price.
2. Determine the profit function, P(x)
3. For what range of items does this company earn money?
4. How many items should the company plan to produce in order to maximize profit?
5. Determine the marginal cost function, marginal revenue function, and marginal profit function.
6. Determine the average cost function, average revenue function, and average profit function.
7. Determine functions for marginal average cost, marginal average revenue, and marginal average profit.
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