Step 1 :The problem is asking for the difference between the revenue and cost for the company when they sell 300 radios. This difference is also known as the profit. To find this, we need to substitute x=300 into both the revenue and cost functions, and then subtract the cost from the revenue.
Step 2 :Substitute x=300 into the revenue function: \(R(300)=41*300=12300\)
Step 3 :Substitute x=300 into the cost function: \(C(300)=15000+20*300=21000\)
Step 4 :Calculate the profit by subtracting the cost from the revenue: \(R(300)-C(300)=12300-21000=-8700\)
Step 5 :The profit when the company sells 300 radios is negative, which means the company is making a loss. This is because the cost of producing and selling the radios is more than the revenue generated from selling them.
Step 6 :Final Answer: The value of \(R(300)-C(300)\) is \(\boxed{-8700}\). This means the company makes a loss of $8700 when they sell 300 radios.