This is a continuation of the DIXI bikes problem given in Assignments $1.$ Here is some additional information. Many of the DIXI customers are expecting or even demanding very short response times, as that is what attracted them to DIXI Bikes in the first place. This condition, in addition to the volatility of overall demand, has put a strain on capacity planning. The company finds that at times there is a lot of idle time $($adding significantly to costs$),$ whereas at other times the demand exceeds capacity and hurts customer response time. The inventory problem has continued to be a challenge. It is becoming apparent that the current storage space which is limited to $900$ units is being fully utilized in certain months and additional storage space might be needed. While that is a cost that the company would like to avoid if possible, additional space can be rented in a close$-$by warehouse for $$24,000$ per year for each block of $100$ units $($$$20/$bike$/$month$),$ provided that this is a viable option. Another problem the company is facing is the volatility of demand for bikes. Since they are worried about unproductive idle time and yet does not wish to lay off any of the $30$ workers they currently have during times of low demand. The company has allowed them to continue to work steadily and build finished goods in the low season and use overtime in the high season, but they are unsure of the economic impact of this policy. This policy makes the problem of building the "right" finished goods in the right quantity even more challenging, especially given the tight availability of storage space. In any case, the company has prepared a severance package equivalent to one month$$s salary $($based on the last month worked$)$ if it ever becomes necessary to lay off some workers in low demand seasons. The company has a policy to meet the demand on time. In the past year they held on the average $800$ units of monthly inventory and produced a total of $757$ units in overtime, resulting in a total cost of about $$2,800,000($which includes Labour, Hiring, Layoff, Inventory and Overtime costs$).$ Here is some additional data: Beginning inventory $($for the new period$)$: $190$ units Inventory Holding cost: $$10$ per bike per month Regular time labour cost: $$240$ per working day $(8$ hr shift$).$ Overtime is limited to a maximum of $25\%$ of regular time and the overtime labour costs $1\mathrm{.}5$ times the regular time labour. Hiring cost $$1800$ per employee. The other mossing data and information can be extracted from the case details above. The production department has been having some success in projecting the demand for its products, as given below, and seeking your help to create a SOP to assist it future MPS plan. The projected forecasts for the bikes product family for periods t$=61-72($year $6)$ and number of days in each month are given below. Forecasts for t$=73($first month of year $6)$ is also given just in case you need it$.$ T$=61$ T$=62$ T$=63$ T$=64$ T$=65$ T$=66$ T$=67$ T$=68$ T$=69$ T$=70$ T$=71$ T$=72$ T$=73783773123013301662162114301366111597069195459322202020212320222215232022$ Requirements: Assignment $2$: Due, February $15.$ a$)$ Propose a chase SOP and a level SOP for the next $12$ months $($Year $6).$ b$)$ Briefly summarize each plan in a table and discuss their main characteristics in contrast with each other. Between these three plans, which plan would you recommend the company to choose? Justify your recommendation.