(−2) 2a 2 −4 The vertex is (8, 64). The maximum product is 64. 20 20 10 x b = − = − = − = This occurs when the two numbers are 8 and 16 8 8 . − = When the width is 150 feet, the length is x = 62. Let = one of the numbers 600 2 (150) 600 300 300 feet. x − = − = Let 20 = the other number x The dimensions of the rectangular plot with maximum – area are 150 feet by 300 feet. This gives an area of ( ) (20 ) 20 P x x x x x2 = − = − = −x2 + 150 300 45, 000 square feet. ⋅ = 20x (−1) 2a 2 −2 The other number is 20 20 10. x − = −10 = The numbers which maximize the product are 10 and 10. The maximum product is 10 100. ⋅10 =
2a 2 (−2) −4 The vertex is (8, 64). The maximum product is 64. This occurs when the two numbers are 8 and 16 − 8 = 8 . 62. Let x = one of the numbers Let 20 – x = the other number P ( x ) = x (20 − x ) = 20 x − x2 = −x2 + 20x x = − b = − 20 = − 20 = 10 When the width is x = 150 feet, the length is 600 − 2 (150) = 600 − 300 = 300 feet. The dimensions of the rectangular plot with maximum area are 150 feet by 300 feet. This gives an area of 150 ⋅ 300 = 45, 000 square feet. 2a 2 (−1) −2 The other number is 20 − x = 20 −10 = 10. The numbers which maximize the product are 10 and 10. The maximum product is 10 ⋅10 = 100.
Precalculus-Essentials-5th-Edition-Blitzer-Solutions-Manual.docx