A precast concrete manufacturing company produces $10,000$ beams per annum. The cost to manufacture at this rate is $$50,000$ for materials, $$80,000$ for labor and $$57,000$ fixed costs per annum payable at the beginning of each year $($just the fixed costs$).$

$-$ Suppose that we are expecting a minimum profit of $$63,000$ a year. For how much should we sell each beam?

$-$ If we produce only $6000$ beams with the selling price you calculated, is the company still making profit? How about $4000?$ Plot the break$-$even graph and find the break$-$even point.