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An artisan makes hand-crafted painted benches to sell at a craft mall. Her weekly revenue...

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Accounting

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
(a) Find a quadratic model for revenue. (Round all numerical values to three decimal places.)
R(n)=-10.857n2+91.714n, dollars
Find a cubic model for cost. (Round all numerical values to three decimal places.)
C(n)=
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(n)=
dollars
(b) Write the derivative formula for profit.
P'(n)=
per bench
(c) Find and interpret the rates of change of profit when the artisan sells 5,9, and 10 benches, respectively. (Round your answers to two decimal places.)
P'(5)=q
per bench
When the artisan makes 5 benches, the profit is
by $
| per bench.
P'(9)=$
per bench
When the artisan makes 9 benches, the profit is
|by $[,] per bench.
P'(10)=$
per bench
When the artisan makes 10 benches, the profit is --- Select--vv by $ per bench.
(d) Use the information in part (c) to determine the number of benches the artisan should produce each week for maximum profit.
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