Break-Even Analysis You are setting up a part-time business with aninitial investment of $21,000. The unit cost of the product is $11.50, and the selling price is $19.90. (a) Find equations for the total cost C (in dollars) and total revenue R (in dollars) for x units. (b) Find the break-even point by finding the point of intersection of thecost and revenue equations. (c) How many units would yield a profit of $1000?

Real-World Applications 40. A car rental package costs $70/week, with an additional charge of $0.15/mile beyond 200 miles. The cost formula would be C = $70 + 0.15 (x – 200). If you have to keep your bill lower than $125, what is the maximum distance (in miles) beyond 200 miles you can drive?

Maximizing Profits The quantity demanded each month of the Walter Serkin recording of Beethoven's Moonlight Sonata, produced by Phonola Media, is related to the price per compact disc. The equation p = 0.00044x +9 (0 ≤ x ≤ 12,000) where p denotes the unit price in dollars and x is the number of discs demanded, relates the demand to the price. The total monthly cost (in dollars) for pressing and packaging x copies of this classical recording is given by C(x) = 600 + 2x - 0.00003x²2 (0≤x≤ 20,000). To maximize its profits, how many copies should Phonola produce each month? Hint: The revenue is R(x) = px, and the profit is P(x) = R(x) - C(x). (Round your answer to the nearest whole number.) X discs/month