The annual profit from the sales of an item is equal to the annual revenue minus the annual cost for that item. The revenue from that item is equal to the number of units sold times the price per unit. If n units of a portable heart monitor were sold in 2012 at a price of 65 each, and the annual cost to produce n units was (20,000+10n) , then which of the following statements indicates that the total profit for this heart monitor in 2012 was greater than 500,000 A) 500,000lt 55n-20,000 B) 500,000gt 55n-20,000 C) 500,000lt 55n+20,000n D) 500,000lt 75n-20,000n

To determine which statement indicates that the total profit for the heart monitor in 2012 was greater than $\$ 500,000$, we need to calculate the total profit and compare it to $\$ 500,000$.<br /><br />The total revenue from selling $n$ units at a price of $\$ 65$ each is $65n$. The annual cost to produce $n$ units is $20,000 + 10n$. Therefore, the total profit is the total revenue minus the total cost, which is $65n - (20,000 + 10n)$.<br /><br />Simplifying this expression, we get $65n - 20,000 - 10n$, which simplifies further to $55n - 20,000$. <br /><br />Therefore, the total profit for the heart monitor in 2012 is $55n - 20,000$. <br /><br />To indicate that the total profit was greater than $\$ 500,000$, we need the inequality $55n - 20,000 > 500,000$. <br /><br />Solving this inequality, we get $55n > 520,000$, which simplifies to $n > \frac{520,000}{55}$. <br /><br />Therefore, the correct statement is A) $500,000 < 55n - 20,000$, as it indicates that the total profit for the heart monitor in 2012 was greater than $\$ 500,000$.