Dime a dozen diamonds makes synthetic diamonds by treating carbon. Each diamond can be sold for $$100.$ The material cost for the standard diamond is $$30$$$.$ The fixed costs for the factory and admin expenses is $$200,000$ a year. The machinery costs $$1$ 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? $($b$)$What is the NPV break$-$even level of diamonds sold per year assuming a tax rate of $35\%,$ a $10-$year project life, and a discount rate of $12\%?$