Question

A chain of hardware stores finds that the demand D for a special power tool varies inversely with the advertised price P of the tool. Suppose that when the price is advertised at $85, there is a monthly demand for 10000 units at all participating stores. Important Note: MapleTA doesn't recognize commas in big numbers, so don't include them in your answers. (a) Find the proportionality constant k. k =

(b) Determine the variation equation (include the value of k you found in part (a), not the letter k itself.)

(c) Find the projected demand if the price was lowered to $70.83. Round to a whole number, but keep the context of the problem in mind (Does it make sense to round up?). D =

(d) Find the price that will result in a projected demand of 12500 units per month. P = $

Answer 1

Date det D be the demand and P be the Price Phen given that Vanas ImVausely demand to Pricu DaI or D=K- DP K DAP=DaP advahsed Price p for a 85 dhe monthly demand b100o0 K DD K= 1000OX85 K= 8500 00 The variahon lquation by DP= 850000 Ck- 8s0000) CIthe Piu Pwas lowered to P8 70.83 then the projected demand D.C70.83) 8 S000O 850000 12000,56 76. 83 OT 12001 CTounded D =12006 Projected demand d) Finding th Price P for D18500 PP= 8500OD 2 500P 850060 850000 P = 68 12500 P $168 the Prica 21