Question 5 of 25 Step 1 of 1 No Time Limit Lee is opening an online shop to sell handmade necklaces. He has determined that his cost and revenue functions are \( \mathrm{C}(\mathrm{x})=590+24 \mathrm{x} \) and \( R(x)=71 x \), respectively, where \( x \) represents the number of necklaces. Write the profit function, \( P(x) \), for Lee's business. Answer 2 Points Keypad Keyboard Shortcuts \[ P(x)=\square \] Next

To find the profit function \( P(x) \), we need to subtract the cost function \( C(x) \) from the revenue function \( R(x) \). So we have: \[ P(x) = R(x) - C(x) = 71x - (590 + 24x) \] This simplifies to: \[ P(x) = 71x - 590 - 24x = 47x - 590 \] Now, you can write the profit function: \[ P(x) = 47x - 590 \] --- In the world of e-commerce, Lee's handmade necklace shop illustrates the classic business model – sell for more than the cost! The combination of revenue and cost functions is a fundamental concept in running any online venture. If Lee sells at least 13 necklaces, he’ll start making a profit, as that's when \( P(x) \) becomes positive! For anyone trying to embark on a similar venture, remember to account for all costs, including material, shipping, and even website fees. Often, new entrepreneurs overlook these, leading to unexpected losses. Understanding this can make the difference between thriving in the market and closing shop!