A subscription food box service, GoldBelly, is planning to launch a new line of boxes. Each month the subscriber will receive $($or be able to send$)$ a particular type of food item from the best restaurants around the USA. The four boxes they are going to add are cookie, icecream, pie, and cake. It will cost the company about $$50,000$ to coordinate the boxes, and $$125,000$ in marketing. The prices and variable costs of the models are: Pcookie $=$ $$50,$ VCcookie $=$ $$15$; Picecream $=$ $$90,$ VCicecream $=$ $$25$; Ppie $=$ $$65,$ VCpie $=$ $$18$; and Pcake$=$ $$75,$ VCcake $=$ $$22.$ They expect to sell the models in the ratio $7$:$4$:$5$:$3,$ respectively. The total customer base of GoldBelly is $10,400$ customers. a$.$ If GoldBelly has $$250,000$ to spend on increasing the retention rate in the segment with the highest CLV$,$ what would the retention rate need to increase to$,$ in order to justify spending that amount on retention. $($Hint: Number of customers would be the sales mix fraction times the total customer base. Find the new M by subtracting $$250,000/$number of customers in that segment. Rearranging the CLV formula in terms of r gives the following$).[3]$ b$.$ Again, just looking at the highest CLV segment, suppose that instead of spending the whole $$150,000$ on the ad buy, GoldBelly decided to spend a portion on ads, and some towards coupons. Of course, not everyone will redeem the coupon, but they expect to gain at least $600$ of those customers with an offer of a $$10$ coupon, or at least $4,500$ if they offer a $$5$ coupon. Assuming that spending the $$150,000$ on advertising would have brought in $3,000$ customers:a$.$ Calculate the new CLV for each option $[3]$:$1.$ $$150,000$ on ads$2.$ $$100,000$ on ads and a $$10$ coupon$3.$ $$115,000$ on ads and a $$5$ couponb. Calculate the total segment value for those new customers for each option from part $($i$).$