A restaurant chain plans to introduce a new buffalo steak dinner. Managers tested various prices in their establishments and arrived at the following estimates:
Price "p" $14.95 $19.95 $24.95 $29.95
each week "x" 2800 2300 1600 300
a) Fit a quadratic function that gives demand as a function of price.
b) Find the price per dinner that results in the sale of 2600 buffalo steak dinners.
c) Using the function found in part (a), find a function for revenue as a function of price.
d) Plot the graph of revenue.
e) Using derivatives, find the price at which revenue is maximized. What is the maximum revenue? How many buffalo dinners will be sold each week at this price?
f) If menus are printed with the optimal price (found in part (e)) mistakenly reduced by $1, what is the loss in revenue? Is this a big deal? Should you fire the printer?