Die yield = Wafer yield x 1/(1 + Defects per unit area x Die area) ^N

Chip	Die Size (mm2)	Estimated defect rate (per cm2)	N	Manufacturing size (nm)	Transistors (billion)	Cores
BlueDragon	180	0.03	12	10	7.5	4
RedDragon	120	0.04	14	7	7.5	4
Phoenix	200	0.04	14	7	12	8

Figure 1.26

Your colleague at AMD suggests that, since the yield is so poor, you might make chips more cheaply if you released multiple versions of the same chip, just with different numbers of cores. For example, you could sell Phoenix⁸, Phoenix⁴, Phoenix², and Phoenix¹, which contain 8,4,2 and 1 cores on each chip, respectively. If all eight cores are defect-free, then it is sold as Phoenix⁸. Chips with four to seven defect-free cores are sold as Phoenix⁴, and those with two or three defect-free cores are sold as Phoenix². For simplification, calculate the yield for a single core as the yield for a chip that is 1/8 the area of the original Phoenix chip. Then view that yield as an independent probability of a single core being defect free. Calculate the yield for each configuration as the probability of at the corresponding number of cores being defect free.

1. If it previously cost $20 dollars per chip to produce Phoenix⁸, what will be the cost of the new Phoenix chips, if there are no additional costs associated with rescuing them from the trash?

2. You currently make a profit of $30 for each defect-free Phoenix⁸, and you will sell each Phoenix⁴ chip for $25. How much is your profit per Phoenix⁸ chip if you consider (i) the purchased price of Phoenix⁴ chips to be entirely profit and (ii) apply the profit of Phoenix⁴ chips to each Phoenix⁸ chip in proportion to how many are produced?