(Solution) - The Ali Baba Co is the only supplier of a -(2025 Original AI-Free Solution)

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The Ali Baba Co is the only supplier of a particular type of Oriental carpet. The estimated demand for its carpets is Q = 112,000 ? 500P + 5M, Where Q = number of carpets, P = price of carpets (dollar per unit), and M = consumers income per capita. The estimated average variable cost function for Ali Baba?s carpets is AVC = 2000 ? 0.012Q + 0.000002Q2.
Consumer?s income per capita is expected to be $20,000 and total fixed cost is $100,000.
1. How many carpets should the firm produce in order to maximize profit?
2. What is the profit maximizing price of carpets?
3. What is the maximum amount of profit that the firm can earn selling carpets?
4. Answer parts a through c if consumer?s income per capita is expected to be $30,000 instead.