webassignnet Apple Google ApplyingToColiege [a .1 . mm W An artisan makes hand-craed 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 I Weekly cost, C sold each week, In (dollars) (dollars) 1 293 I 59 3 873 88 5 98 7 128 9 1982 145 11 1955 I 192 13 1707 I 216 (a) Find a quadratic model for revenue. (Round all numerical values to three decimal places.) R(n)= 21.150n2+420.04n147.81 \\/ dollars Find a cubic model for cost. (Round all numerical values to three decimal places.) C(Il) = 2.460n3 63.5992 + 611.169n + 365.091 x dollars Using the previous models for revenue and cost, find a cubic model for profit, P. (Round all numerical values to three decimal places.) P(rl)= 2.460 + 57.249n2 7 191.129n 7 519.902 x dollars (b) Write the derivative formula for profit. Pin) = 7.38n2+ 114.498n191.129 x per bench (c) Find and interpret the rates of change of profit when the artisan sells 6, 9, and 10 benches, respectively. (Round your answers to two decimal places.) P'(6) : $ 11.44 x per bench When the artisan makes 6 benches, the prot is increasing a \\/ by $ per bench. P'(9) 2 $ 3.96 X per bench When the artisan makes 9 benches. the prot is increasino a / bv $ 3.96 )1 Der bench