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An artisan makes hand-crafted painted benches to sell at a craft mall. Her weekly revenue and costs (not including labor) are given in the table. Weekly Revenue and Costs for Hand-crafted Benches Number of benches Weekly revenue, R Weekly cost, C sold each week, :1 (dollars) (dollars) 1 298 57 3 872 90 5 1367 103 7 1754 123 9 1976 139 11 1953 191 13 1706 214 (3) Find a quadratic model for revenue. (Round all numerical values to three decimal places.) R01) = |:| dOIIarS Find a cubic model for cost. (Round all numerical values to three decimal places.) Using the previous models for revenue and cost, find a cubic model for profit, P. (Round all numerical values to three decimal places.) P(n)= dollars (b) Write the derivative formula for prot. P'(n) = per bench (c) Find and interpret the rates of change of prot when the artisan sells 7, 9, and 10 benches, respectively. (Round your answers to two decimal places.) P'(7) = $ per bench When the artisan makes 7 benches, the prot is by $ :] per bench. P'(9) = $ per bench When the artisan makes 9 benches, the prot is by $ :] per bench. PM) = $ :] per bench When the artisan makes 10 benches, the prot is by $ :] per bench. (d) Use the information in part (c) to determine the number of benches the artisan should produce each week for maximum prot. benches