Question

please answer correctly to 10-significant digits

(1 point) The managers of a furniture store have compiled data showing the daily demand for recliners at various prices. Recliner price (S) 399 Demand (recliners) 62 422 599 47 699 40 799 34 Revenue (S) (a) In the table above, fill in the revenue generated by selling the number of recliners at the corresponding price. Do not include dollar signs or commas in your answers. (b) Using least-squares regression, find the quadratic function for the revenue as a function of the price p that best fits the data. (c) According to the quadratic function you found in (b), what price should the store charge for their recliners to maximize revenue? (do not include commas and round to the nearest dollar) (d) What is the maximum revenue at this price? (do not include commas and round to the nearest dollar)

Answer 1

Quadratic regression equation, Y = Ax^2 + Bx + c. Y = -0.056.45 x^2 -1172.9901 x + 4799.05455^-1 To maximize revenue, price (x) = -B/2A = -72.9901/2(-0.5645)) = 637.73251 = $ 630 y = 0.05645 (630)62 + 72.9901 (630) + 9749.85453 therefore $ 741300.27615