Green lawns provides a lawn fertilizer and weed control service. the company is adding a special aeration treatment as alow-cost extra service option that it hopes will attract new customers. management is planning to promote this newservice in two media: radio and direct-mail advertising. a media budget of $3.000 is available for this promotionalcampaign. based on past experience in promoting its other services, green lawns has obtained the following estimate ofthe relationship between sales and the amount spent on promotion in these two media. s= —2r2— iomi—8rm+ ibr+34mwhere5 = total sales in thousands of dollarsr: thousands of dollars spent on radio advertisingm = thousands of dollars spent on direct-mail advertisinggreenlawns would like to develop a promotional strategy that will lead to maximum sales subject to the restrictionprovided by the media budget. a. what is the value of sales if $2,000 is spent on radio advertising and $1,000 is spent on direct-mail advertising? b. formulate an optimization problem that can be solved to maximize sales subject to the media budget of spending nomore than $3,000 on total advertising. c. determine the optimal amount to spend on radio and direct-mail advertising. how much in sales will be generated?