An artisan makes handcrafted 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 Handcrafted Benches
a Find a quadratic model for revenue. Round all numerical values to three decimal places.
dollars
Find a cubic model for cost. Round all numerical values to three decimal places.
dollars
Using the previous models for revenue and cost, find a cubic model for profit, Round all numerical values to three decimal places.
dollars
b Write the derivative formula for profit.
per bench
c Find and interpret the rates of change of profit when the artisan sells and benches, respectively. Round your answers to two decimal places.
per bench
When the artisan makes benches, the profit is
by $
per bench.
$
per bench
When the artisan makes benches, the profit is
by $ per bench.
$
per bench
When the artisan makes benches, the profit is Select 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.
