Questions: A company that sells radios has yearly fixed costs of 600,000. It costs the company 40 to produce each radio. The radio will sell for 60. The company's costs and revenue are modeled by the following functions, where x represents the number of radios produced and sold. C(x)=600,000+40x, R(x)=60x Find and interpret (R-C)(15,000), (R-C)(30,000), and (R-C)(45,000). (R-C)(15,000)=-300,000 What is the meaning of (R-C)(15,000) ? A. If the company sells 300,000 radios in one year, its net loss is 15,000. B. If the company sells 15,000 radios in one year, its net profit is 300,000. C. If the company sells 300,000 radios in one year, its net profit is 15,000. D. If the company sells 15,000 radios in one year, its net loss is 300,000.

The company incurs a loss of $-300000 after selling 15000 items.

The total cost, $C(x)$, for producing 30000 items is calculated by adding the fixed costs, $f$, to the product of the variable cost per item, $v$, and the number of items, $x$. \[C(x) = f + v \cdot x = 600000 + 40 \cdot 30000 = 1800000\]

The total revenue, $R(x)$, from selling 30000 items is calculated by multiplying the selling price per item, $p$, by the number of items, $x$. \[R(x) = p \cdot x = 60 \cdot 30000 = 1800000\]

The profit or loss is found by subtracting the total cost, $C(x)$, from the total revenue, $R(x)$. \[\text{Profit or Loss} = R(x) - C(x) = 1800000 - 1800000 = 0\]

The company breaks even, neither making a profit nor incurring a loss.

The total cost, $C(x)$, for producing 45000 items is calculated by adding the fixed costs, $f$, to the product of the variable cost per item, $v$, and the number of items, $x$. \[C(x) = f + v \cdot x = 600000 + 40 \cdot 45000 = 2400000\]

The total revenue, $R(x)$, from selling 45000 items is calculated by multiplying the selling price per item, $p$, by the number of items, $x$. \[R(x) = p \cdot x = 60 \cdot 45000 = 2700000\]

The profit or loss is found by subtracting the total cost, $C(x)$, from the total revenue, $R(x)$. \[\text{Profit or Loss} = R(x) - C(x) = 2700000 - 2400000 = 300000\]