Dime$-$a$-$Dozen Diamonds makes synthetic diamonds by treating carbon. Each diamond can be sold for $$280.$ The materials cost for a

synthetic diamond is $$220.$ The fixed costs incurred each year for factory upkeep and administrative expenses are $$2,900,000.$ The

machinery costs $$1\mathrm{.}54$ million and is depreciated straight$-$line over $10$ years to a salvage value of zero.

a$.$ What is the accounting break$-$even level of sales in terms of number of diamonds sold? $($THE ANSWER IS $50,900)$

b$.$ What is the NPV break$-$even level of sales assuming a tax rate of $35\%,$ a $10-$year project life, and a discount rate of $12\%?$

Note: Do not round intermediate calculations. Round your final answer to the nearest whole number.