20,000 y = = 5 4,000 the year. The company will minimize its total cost by making 4,000 DVDs five times during Matched Problem 8 Repeat Example 8 if it costs $250 to set up a production run and $0.40 to store a DVD for one year. Exercises 4.6 Skills Warm-up Exercises B 19. Maximum revenue and profit. A company manufactures W In Problems 1-3, express the given quantity as a function f(x) of one variable x. (If necessary, review Section 1.1). and sells x smartphones per week. The weekly price-demand and cost equations are, respectively, 1. The product of two numbers x and y whose sum is 28 P = 500 - 0.4x and C(x) = 20,000 + 20x 2. The sum of two numbers x and y whose product is 36 (A) What price should the company charge for the phones, 3. The area of a circle of diameter x and how many phones should be produced to maximize the weekly revenue? What is the maximum weekly revenue? 4. The volume of a sphere of diameter x (B) What is the maximum weekly profit? How much should 5. The volume of a right circular cylinder of radius x and height the company charge for the phones, and how many equal to the radius phones should be produced to realize the maximum 6. The volume of a right circular cylinder of diameter x and weekly profit? height equal to twice the diameter 20. Maximum revenue and profit. A company manufactures 7. The area of a rectangle of length x and width y that has a and sells x cameras per week. The weekly price-demand and perimeter of 120 feet cost equations are, respectively, 8. The perimeter of a rectangle of length x and width y that has p = 400 - 0.5x and C(x) = 2,000 + 200x an area of 200 square meters (A) What price should the company charge for the cameras, and how many cameras should be produced to maximize A 9. Find two numbers whose sum is 13 and whose product is a the weekly revenue? What is the maximum revenue? maximum. 10. Find two numbers whose sum is 19 and whose product is a (B) What is the maximum weekly profit? How much should the company charge for the cameras, and how many maximum. cameras should be produced to realize the maximum 11. Find two numbers whose difference is 13 and whose product weekly profit? is a minimum. 21. Maximum revenue and profit. A company manufactures 12. Find two numbers whose difference is 19 and whose product and sells x television sets per month. The monthly cost and is a minimum . price-demand equations are 13. Find two positive numbers whose product is 13 and whose C(x) = 72,000 + 60x sum is a minimum. p = 200 - X 0 S x s 6,000 14. Find two positive numbers whose product is 19 and whose 30 sum is a minimum. (A) Find the maximum revenue. 15. Find the dimensions of a rectangle with an area of 200 square (B) Find the maximum profit, the production level that will feet that has the minimum perimeter. realize the maximum profit, and the price the company 16. Find the dimensions of a rectangle with an area of 108 square should charge for each television set. feet that has the minimum perimeter. (C) If the government decides to tax the company $5 for 17. Find the dimensions of a rectangle with a perimeter of each set it produces, how many sets should the company 148 feet that has the maximum area. manufacture each month to maximize its profit? What is 18. Find the dimensions of a rectangle with a perimeter of 76 feet the maximum profit? What should the company charge for each set? that has the maximum area