Advertising Project: A company that makes soft drinks introduces a new product. The

Chapter 7, Problem 8

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Advertising Project: A company that makes soft drinks introduces a new product. The companys salespeople want to predict B, the number of bottles per day they will sell as a function of t, the number of days since the product was introduced. One of the parameters is the amount per day spent on advertising. Here are some assumptions the salespeople make about future sales. The dependent variable is B; the independent variable is t, in days (Figure 7-3m). Figure 7-3m They spend a fixed amount, M, in dollarsper day, to advertise this soft drink. Part of M, an amount proportional to B, isused to maintain present users of this softdrink (Figure 7-3n). The rate of change of B, dB/dt, is directly Advertising costs need to be $80 per day towarm water to 140F, to 160F, and to 180F.say, 155F (when the heat turns on again).Figure 7-3nproportional to the rest of M.maintain sales of 1000 bottles per day. Due to advance publicity, dB/dt will be500 bottles per day when t = 0, independentof M.Use what youve learned in this section to findan equation for B as a function of t. Then showthe effect of spending various amounts, M, onadvertising. (Calculations and graphs would beconvincing.) You might include suchinformation as whether sales will continue togo up without bound or will eventually leveloff. To make an impression on management,assume a certain price per bottle and indicatehow long it will take the product to startmaking a profit