Step 1 :Given the revenue function \(R(x) = 0.21x\) and the profit function \(P(x) = 0.086x - 1.3\), we can find the cost function by subtracting the profit function from the revenue function. This gives us \(C(x) = R(x) - P(x)\).
Step 2 :Substituting the given functions into the equation, we get \(C(x) = 0.21x - (0.086x - 1.3)\). Simplifying this equation gives us the cost function \(C(x) = 0.124x + 1.3\).
Step 3 :To find the cost of producing 7 units, we substitute \(x = 7\) into the cost function. This gives us \(C(7) = 0.124*7 + 1.3 = 2.168\). So, the cost of producing 7 units is \$2.168$ million.
Step 4 :The break-even point occurs when the profit is zero. So, we need to solve the equation \(P(x) = 0\) for \(x\). This gives us \(0.086x - 1.3 = 0\). Solving for \(x\) gives us \(x = 15.116\). So, the break-even point occurs when about 15.116 units are sold.
Step 5 :Final Answer: \(\boxed{C(x) = 0.124x + 1.3}\), \(\boxed{\text{The cost of producing 7 units is } \$2.168 \text{ million}}\), \(\boxed{\text{The break-even point occurs when about 15.116 units are sold}}\)