Apple's smartphone division wants to plan its production in the Shenzhen, China, plant for one of its major product lines { iPhone 13 { for the year 2022. With the goal of entering the refurbished smartphone market, Apple has designed iPhone 13 in such a way that consumer returns can be easily disassembled, remanufactured, and remarketed. Currently, Apple's lenient return policy allows its consumers to return their devices for a full refund within one month of purchase. Apple needs to decide whether the returned devices should be remanufactured to meet the demand of its price-sensitive customers. The forecast demand values for new and refurbished versions of iPhone 13 were nalized in the last S&OP meeting of 2021 as in the following table: Month New Refurbished January 35000 1000 February 30000 2000 March 20000 3000 April 25000 3000 May 20000 4000 June 25000 4000 July 20000 5000 August 25000 5000 September 20000 4000 October 20000 3000 November 15000 3000 December 10000 2000 (a) (40 points) Consider the production planning of new devices only. The smartphones are assembled with a special equipment that can only be leased for one or more months. One such equipment can assemble 1000 items per month and the leasing cost is $70000 per equipment per month. Once the equipment is leased, it should be congured for the assembly process. The conguration cost is $30000 per equipment. The leasing duration can start at the beginning of any month but its termination before the end of 2022 results in an additional fee of $15000 per equipment. The equipment may be underutilized within the leasing duration but overtime production is not permitted. Apple has no such equipment at the end of 2021. Since Apple has a very strong loyal customer base, any demand that is not satised on time is backlogged, incurring a unit cost of $40 per month. However, Apple suspects that the competitor rms will introduce similar smartphones by the end of 2022. The senior executives want to clear all backlogs at the end of 2022, if any, in order to prevent those customers from switching to the other rms' devices. Apple has no inventory at the end of 2021 and wants to have no inventory at the end of 2022. The inventory holding cost for one unit of new device is $25 per month. Formulate a linear program to calculate the optimal number of devices that should be assembled and the optimal number of equipment that should be leased in each month. Solve this linear program using the Excel Solver. (Assume that a fractional number of the equipment can be leased.)

(b) (40 points) Now consider the production planning of new and refurbished devices together. The equipment leased is capable of assembling new devices as well as disassembling and remanufacturing consumer returns. Each equipment can be used in either the assembly line or the remanufacturing line in any month. It can assemble 1000 new devices per month or remanufacture 800 returns per month. The equipment used for one of the two lines in any month can be congured for the other line in the next month at no cost. Remanufacturing operations are constrained by consumer returns. Apple estimates that 20% of the new devices sold in any month will be returned by consumers at the beginning of the next month (within the time period allowed by the lenient return policy). All these returns will become available for remanufacturing (starting in February). Any unmet demand for refurbished devices is backlogged, incurring a unit cost of $10 per month. Apple aims to clear all backlogs for both devices at the end of 2022 due to the approaching competition in the market. Apple has no inventory for either device at the end of 2021 and wants to have no inventory for either device at the end of 2022. The inventory holding cost for one unit of refurbished device is $5 per month. Formulate a linear program to calculate the optimal number of new devices that should be assembled, the optimal number of returns that should be remanufactured, and the optimal number of equipment that should be leased and their optimal allocation between the two product lines in each month. Solve this linear program using the Excel Solver. (Assume that a fractional number of the equipment can be leased.) (c) (20 points) The unit selling prices of new and refurbished devices are $700 and $400, respectively. The unit manufacturing costs (excluding the equipment costs) of new and refurbished devices are $450 and $100, respectively. Based on your ndings in parts (a) and (b), should Apple enter the refurbished smartphone market? Why or why not? Note that Apple must provide a full refund for each returned device even if they do not remanufacture it.

Please correctly answer at least one of the sections.