Question 156344
total cost of production is 500 + (x * 6.5) where x is the number of units sold.

total money realized from sale is (x * 7.4).

total cost must be < total sale so equation becomes ..............

500 + (x * 6.5) < (x * 7.4)

which becomes 500 < (7.4x - 6.5x) 

which becomes 500 < .9x

which becomes (500 / .9) < x

which makes x > 555.55 rounded to > 556 units (partial units not possible).

testing..............

revenue = 555 * 7.4 = 4107;  cost = 555 * 6.5 = 3607.5 + 500 = 4107.5 so no profit because cost is greater then revenue.

revenue = 556 * 7.4 = 4114.5;  cost = 556 * 6.5 = 3614 + 500 = 4114 so profit is made because revenue is greater than cost.