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 Weekly revenue, R Weekly cost, c (dollars) Number of benches sold each week, n (dollars) 1 299 56 868 87 1376 100 1760 129 1984 140 11 1953 190 13 1694 220 (a) Find a quadratic model for revenue. (Round all numerical values to three decimal places.) R(n) = dollars Find a cubic model for cost. (Round all numerical values to three decimal places.) C(n) = dollars

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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
Weekly revenue, R
(dollars)
Weekly cost, C
(dollars)
Number of benches
sold each week, n
1
299
56
3
868
87
1376
100
7
1760
129
1984
140
11
1953
190
13
1694
220
(a) Find a quadratic model for revenue. (Round all numerical values to three decimal places.)
R(n) =
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 3, 9, and 10 benches, respectively. (Round your answers to two decimal places.)
P'(3) = $
per bench
When the artisan makes 3 benches, the profit is increasing v by $
per bench.
Transcribed Image Text: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 Weekly revenue, R (dollars) Weekly cost, C (dollars) Number of benches sold each week, n 1 299 56 3 868 87 1376 100 7 1760 129 1984 140 11 1953 190 13 1694 220 (a) Find a quadratic model for revenue. (Round all numerical values to three decimal places.) R(n) = 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 3, 9, and 10 benches, respectively. (Round your answers to two decimal places.) P'(3) = $ per bench When the artisan makes 3 benches, the profit is increasing v by $ per bench.
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