Please share the response and spreadsheet, or screen prints of solvers and other functions used to solve this problem.

LeanAutoInc produces two models of cars: a sedan, and an SUV. Over the years, the company successfully implemented a production system that eectively achieved "make-to-order": a vehicle is produced only after a customer had placed a order, and the production plant keeps less than one day's inventory.

As a result of the recent global chip shortage and severe backlogs in the supply chain, LeanAutoInc now has to place orders with their chip supplier 6 months in advance. Each SUV requires a chip A, and each sedan needs one chip B. The chip supplier charges LeanAutoInc $30 for each unit of chip A, and $25 for each unit of chip B.

LeanAutoInc forecasts that the mean quarterly demand 6 months from now would be 100,000 cars for the SUV, and 80,000 cars for the sedan. The standard deviation of the demand is 15,000 and 12,000 for the SUV and the sedan, respectively. The supply chains for other parts needed by LeanAutoInc are reliable and responsive, such that chips are the only factor that can potentially limit LeanAuto's ability to meet customers' demand. Chips that are ordered but not used by the end of a quarter are worth only a half of their purchasing price due to the re-work needed to keep up with the latest technology.

(a) Assume that LeanAutoInc makes a prot of $6000 per vehicle from selling an SUV, and $5000 per vehicle from selling a sedan (these prot margins already incorporate the cost of all parts, including the chips).

(i) To optimize prot, how many units of chip A and chip B would you order from the supplier, for the quarter starting 6 months from now?

(ii) In this case, what are the stock-out probabilities for the SUV and the sedan, respectively?

(b) LeanAutoInc cannot produce an SUV using a chip B, but a sedan can be produced using a chip A. After analyzing the benets of risk-pooling, the company decides to use chip A chips for all SUV and sedan production.

The mean demand for chip A is now 100, 000 + 80, 000 = 180, 000.

Assume that the demand for the SUV is independent to the that for the sedan, the standard deviation of the demand for chip A is 15000 2 + 12000 2 = 19209.37.

To achieve the same stock-out probability as in case (a), how many chip A should LeanAutoInc order per quarter? In other words, if the stock-out probability for the SUV computed in part (a) is x, compute the stocking level for chip A such that the demand for the chip exceeds the stocking level with probability x.

(c) Assume that the plan described in (b) is implemented. When the realized total demand for the SUV and the sedan exceeds the amount of chip A LeanAutoInc has in stock, should the company prioritize the production of the SUV or the Sedan, and why? Do you have any thoughts on further improving the company's chip strategy?

(d) Compare the size of the chip orders placed 6 months in advance by LeanAutoInc, with the amount they would have ordered if they could order after demand is realized. If all auto makers adopt similar strategies, what would be the impact on the supply chain for chips?