give me complete solution to this assignment:

Evaluation of subscription model $($Homework assignment after Session $2)$

As the CEO you are wondering if a subscription$-$based model such as Netflix is the answer to RAD$$s woes. Under such a model, customers would have to subscribe to the service to be able to rent dresses that they like.

A preliminary market survey revealed that RAD can expect about $500$ customers to sign up for the service each month for a subscription fee of $$20$ per month. With every $$10$ dollar per month increase in the subscription fee, the demand decreases by $50$ customers, e$.$g$.,$ with a subscription fee of $$30$ per month, RAD expects $450$ customers to sign up for the service each month, while for a subscription fee of $$50$ per month, RAD expects only $350$ customers will sign up each month. There is also customer churn expected as people$$s tastes and need for fashion rental change, and RAD expects most subscribers to remain subscribed for about $6$ months on average before discontinuing their subscription.

Given the nature of the service, not all subscribers would be renting dresses during the entire time that they are subscribed to the service. The marketing team estimates that on average about $20\%$ of the active subscribers at any point in time are likely to have a rental dress with them $($for example, if say there are $1000$ active subscribers, about $200$ of them have a rental with them currently$).$

Unlike Netflix, you believe RAD should charge a rental fee, in addition to the subscription fee, when a subscriber rents a dress. However, the rental fee could be lower than what it currently is$.$ You are considering charging a rental fee of $$15$ per day to subscribers who rent, with an average rental duration of $10$ days.

You want to understand what the implications of a subscription model would be for profitability of business. Among other things, you are curious to understand,

$1.$ How profitability varies with the subscription price,

$2.$ The impact of conversion rate $(\%$ of active subscribers with a rental$)$ on profitability at

different subscription prices, and

$3.$ How the subscription price that maximizes profitability varies with conversion rate.

Guidelines for the assignment

$1.$ Evaluate the subscription model described above and make a recommendation. Your

recommendation should be backed with the required analysis. Your submission should be

in the form of a report and not just answers to questions given above.

$2.$ You are NOT expected to solve an optimization problem as part of this assignment. The expectation is you will perform a what$-$if analysis for different combinations of the

relevant decisions and$/$or parameters that affect RAD$$s profitability.

$3.$ You can evaluate the subscription model assuming the improvement in the inspection

process $($Option $2$ on pg$.2$ of the case$)$ will be implemented.