reenLawns provides a lawn fertilizing and weed control service. The company is adding a special aeration treatment as a low-cost xtra service option, which it hopes will help attract new customers. Management is planning to promote this new service in two media: radio and direct-mail advertising. A media budget of $4,000 is available for this promotional campaign. Based on past experlence in promoting its other services, GreenLawns has obtained the following estimate of the relationship between sales and the amount spent on promotion in these two media: S=2R210M27RM+20R+37M Where S= total sales in thousands of dollars R= thousands of dollars spent on radio advertising M= thousands of dollars spent on direct-mail advertising GreenLawns would like to develop a promotional strategy that will lead to maximum sales subject to the restriction provided by the media budget. (a) What is the value of raies if $2,000 is spent on radio advertising and $2,000 is spent on direct-mail advertising? Enter amounts in dollars, 1. e. $12 thousands should be written as $12,000 Formulate an optimization problem that can be solved to maximize sales subject to the media budget of spending no more than $4,000 on total advertising. If the constant is " 1" it must be entered in the box. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank (Example: 300 ). If your answer is zero enter " 0 ". Max (c) Determine the optimal amount to spend on radio and direct-mall advertising. How muct sin sales will be generated? Enter amounts in dollars, 1,e.$12 thousands should be written as $12,000. If your answer is zero enter " 0 ". Amount spent on radio advertising =s Amount spent on direct-mail advertising =s Total Sales =