Problem
The figure shows the graphs of the cost and revenue functions of a company that manufactures and sells small radios. Use the formulas below to find $R(400)-C(400)$. Describe what it means for the company. \[ \begin{array}{l} R(x)=43 x \\ C(x)=10,000+21 x \end{array} \] What is the value of $R(400)-C(400)$ ? \[ R(400)-C(400)=\$ \] Which of the following statements best describes what this means for the company? A. The company is losing money because revenue is greater than cost. B. The company is losing money because cost is greater than revenue. C. The company is breaking even because cost and revenue are equal. D. The company is making money because revenue is greater than cost. E. The company is making money because cost is greater than revenue.
Solution
Step 1 ：Given the revenue function \(R(x)=43x\) and the cost function \(C(x)=10,000+21x\), we are asked to find the value of \(R(400)-C(400)\).
Step 2 ：Substitute \(x=400\) into the given formulas for \(R(x)\) and \(C(x)\).
Step 3 ：Calculate \(R(400) = 43 * 400 = 17200\) and \(C(400) = 10000 + 21 * 400 = 18400\).
Step 4 ：Subtract the result of \(C(400)\) from \(R(400)\) to get the profit: \(R(400)-C(400) = 17200 - 18400 = -1200\).
Step 5 ：The result of the calculation is \(-1200\), which means the company is losing money because the cost is greater than the revenue when they manufacture and sell 400 radios.
Step 6 ：\(\boxed{R(400)-C(400) = -1200}\). The company is losing money because cost is greater than revenue.
