【分析】如图3-12，设矩形宽为[tex=1.071x1.286]nA4T6OZKPUZwXG+F4en1WQ==[/tex]，高为[tex=0.571x1.286]Hz6y44ELFVLLNrLVhO3CQA==[/tex]，现在要确定[tex=0.571x1.286]XubEW9+1+hkJqH7jXe5MrA==[/tex]、[tex=0.571x1.286]Hz6y44ELFVLLNrLVhO3CQA==[/tex]（用已知量[tex=0.786x1.286]yokTf2U2Z7kNGUXMm22GjQ==[/tex]、[tex=1.143x1.286]MC1XsYmMZOUQBFxDpyQseQ==[/tex]表出），使[tex=3.5x1.286]Rnuumlq+l5DQYZavDqC4CQ==[/tex]取得最大值。解这类最大、最小的实际问题，关键是建立目标函数，其中选择自变量至关重要，选择的自变量不同，建立的目标函数就不一样，运算起来就会有繁有简。下面提供几种选择自变量的不同方法。[img=230x283]177145a7c9f483d.jpg[/img]（1）取[tex=0.571x1.286]XubEW9+1+hkJqH7jXe5MrA==[/tex]为自变量，如图3-12，[tex=10.143x1.357]Dlflv79h5BJ426qXwWUOK/Zwet1gBMb+WEQPDhbmGZHxv/QCUeWPPw5khb4Wcnpy[/tex]，[tex=12.643x1.357]5dzbfkSQUZz/ovPTOSLcpmYNdMr2Sdui42gsJCa1IHf6oHxOmHsJBCNNwoblGgkR[/tex][tex=7.286x1.286]56Mt4UB0aFLdMt02IaHEZbdfqlACWML+q/1L1FTLcjk=[/tex]；①（2）取[tex=3.429x1.286]gJJ5e/2OdMpE3N70g9va4Q==[/tex]为自变量，则[tex=4.786x1.286]zm++b52Q6bgBUo73t+LfTMJY3jDMJG3o+yh3LFdiSMI=[/tex]，[tex=10.714x1.786]Dlflv79h5BJ426qXwWUOK03HAmtadA41Jp6gJYsRiJ5COGHXmArB+QjZtTyqJVVv[/tex]，[tex=15.0x1.786]azsH0iwAdahEJrVS06YmXaMGLnzF6iu/hmd0f3uQBrrwDkzWo0sqiYd0TfPXN0AlPuVdFxRZpYnMwAIpK/84U/fy0LFDLEWSayZNOm9W6f8=[/tex]，②[tex=6.643x1.286]IinRX+gNig+fSS88EWF87WV0sxBWiT8UPw9PouGkS7o=[/tex]；（3）取[tex=3.286x1.286]aBshh8ytq2K3n2sCbcOOnA==[/tex]为自变量，则[tex=4.5x1.286]TvlN+FsDynpPNnLOmtZ9G+9GnRnzyWdWRtoIIYbvtes=[/tex]，[tex=12.286x1.786]Dlflv79h5BJ426qXwWUOK8NYPHt+nt5uMnC4Px85BBkqCF/KyjpSogzv4ymB+HECsummvvEl6+DX6OItojiK4A==[/tex]，[tex=16.429x1.786]pxbFgFYpbzRxbOXXTuVXRaS8YaMBJVaOdodqnENbvJTMYq2Cm4nIXj4h09slKkyxZlHR5JQpHJqpulkGh7ebG2rSboh9rHWHdHo3a2kHojSDYolJYJP8GB3C3x+PUBX6[/tex]，③[tex=4.357x1.286]zHeCUEZo+p6AbHE5jlf2cQ==[/tex]；（4）取[tex=4.857x1.286]7C+EPEMqsWiSzlu+KNBij7RNNGAULxJslt2+0TDpAjY=[/tex]为自变量，则[tex=4.643x1.286]mAXgDrUT33eYAvuXmjKM4SAZw2KXQsjJW/ZBWPjIHAs=[/tex]，[tex=10.857x1.286]MJwWtIfocmeYN1rXn7Xh9X1D3vLUo8HNddKGdFcoVEib+57btBZmnsWO5J/xJOQ1[/tex]，[tex=14.929x1.286]WTfuFhr1oFz6koXze1Oh8cdewg9K96VR17VvuDXIFCsQf3UHZlN/RRQ8oFjv6KjgThWuWz4fxesFVyDferch25rLuQqr2IrhxuGrRYSgdwM=[/tex][tex=13.286x1.286]Ucj5S9pZII/NvJG3OhSierlv5+NkZBWLoTQUu0+BdbSrpfb2QdF7BwvNnsE1obdJf6/aqEwKloUMHJpySVzrgg==[/tex]，④[tex=4.214x1.286]kzAl8tsaVZzS7enKB04V4+AuYQxLPxucrKXcrQfwf5k=[/tex]。比较上列四种目标函数，①、②、③都带根号，不便于求导等运算；第四种运算方便一些，故应以④作为目标函数求最值。具体运算留给读者练习。答案：[tex=9.286x1.286]e7CAdLJISo6UU6NHAOvLBp+Ke+OudFo4UUUPp8MEb4nwEKnW99AE3yMAdG8qrYF7[/tex]。