Chapter 5: Exercises with Solutions

542 Chapter 5 Quadratic Functions24. Find two numbers whose differenceis 24 and whose product is a minimum.25. One number is 3 larger than twice asecond number. Find two such numbersso that their product is a minimum.26. One number is 2 larger than 5 timesa second number. Find two such numbersso that their product is a minimum.27. Among all pairs of numbers whosesum is −10, find the pair such that thesum of their squares is the smallest possible.28. Among all pairs of numbers whosesum is −24, find the pair such that thesum of their squares is the smallest possible.29. Among all pairs of numbers whosesum is 14, find the pair such that the sumof their squares is the smallest possible.30. Among all pairs of numbers whosesum is 12, find the pair such that the sumof their squares is the smallest possible.31. Among all rectangles having perimeter40 feet, find the dimensions (lengthand width) of the one with the greatestarea.32. Among all rectangles having perimeter100 feet, find the dimensions (lengthand width) of the one with the greatestarea.33. A farmer with 1700 meters of fencingwants to enclose a rectangular plotthat borders on a river. If no fence is requiredalong the river, what is the largestarea that can be enclosed?34. A rancher with 1500 meters of fencingwants to enclose a rectangular plotthat borders on a river. If no fence is requiredalong the river, and the side parallelto the river is x meters long, findthe value of x which will give the largestarea of the rectangle.35. A park ranger with 400 meters offencing wants to enclose a rectangularplot that borders on a river. If no fenceis required along the river, and the sideparallel to the river is x meters long, findthe value of x which will give the largestarea of the rectangle.36. A rancher with 1000 meters of fencingwants to enclose a rectangular plotthat borders on a river. If no fence is requiredalong the river, what is the largestarea that can be enclosed?37. Let x represent the demand (thenumber the public will buy) for an objectand let p represent the object’s unit price(in dollars). Suppose that the unit priceand the demand are linearly related bythe equation p = (−1/3)x + 40.a) Express the revenue R (the amountearned by selling the objects) as afunction of the demand x.b) Find the demand that will maximizethe revenue.c) Find the unit price that will maximizethe revenue.d) What is the maximum revenue?38. Let x represent the demand (thenumber the public will buy) for an objectand let p represent the object’s unit price(in dollars). Suppose that the unit priceand the demand are linearly related bythe equation p = (−1/5)x + 200.a) Express the revenue R (the amountVersion: Fall 2007