The Boston Beer Company Inc. $($SAM$)$ produces Samuel Adams beer and other alcoholic beverages. Boston Beer reported the following operating information for a recent year $($in thousands$)$:

Sales $q,$ $$1,736,432$

Cost of goods sold $q,$

Selling, general, and administrative expenses....

Operating income $q,565,779\frac{(1,487,759)}{\text{\$}248,673}$

$*$Before special items

Details

In addition, assume that Boston Beer sold $7,400$ thousand barrels of peer during the year. Assume that variable costs were $75\%$ of the cost of goods sold and $40\%$ of selling, general, and administrative expenses. Assume that the remaining costs are fixed. For the following year, assume that Boston Beer expects pricing, variable costs per barrel, and fixed costs to remain constant, except that new distribution and general office facilities are expected to increase fixed costs by $$50$ million.

a$.$ Compute the break$-$even number of barrels for the current year, rounded to the nearest thousand. In computing variable and fixed costs, round to the nearest thousand. In computing the per$-$barrel amounts, round to the nearest cent.