全国大学生建模大赛初赛试题
<p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt;"><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体;">.</span><span style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体;">某公司用两种原油（<span lang="EN-US">A</span>或<span lang="EN-US">B</span>）混合加工成两种汽油（甲或乙）。甲，乙两种汽油含原油<span lang="EN-US">A</span>的最低比例分别为<span lang="EN-US">50%</span>和<span lang="EN-US">60%</span>，每吨售价分别为<span lang="EN-US">4800</span>元和<span lang="EN-US">5600</span>元。该公司现有原油<span lang="EN-US">A</span>和<span lang="EN-US">B</span>的库存量分别为<span lang="EN-US">500t</span>和<span lang="EN-US">1000t</span>，还可以从市场上买到不超过<span lang="EN-US">1500t</span>的原油<span lang="EN-US">A</span>。原油<span lang="EN-US">A</span>的市场价为：购买量不超过<span lang="EN-US">500t</span>时单价为<span lang="EN-US">10000</span>元<span lang="EN-US">/t</span>；购买量超过<span lang="EN-US">500t</span>但不超过<span lang="EN-US">1000t</span>时，超过<span lang="EN-US">500t</span>的部分<span lang="EN-US">8000</span>元<span lang="EN-US">/t</span>；购买量超过<span lang="EN-US">1000t</span>时，超过部分<span lang="EN-US">6000</span>元<span lang="EN-US">/t</span>。该公司应如何安排原油的采购和加工。<span lang="EN-US"><p></p></span></span></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt;"><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体;"><p></p></span></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt;"><span style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体;">要求：<span lang="EN-US"><p></p></span></span></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt;"><span style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体;">（<span lang="EN-US">1</span>）问题分析，模型建立，求解模型；<span lang="EN-US"><p></p></span></span></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt;"><span style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体;">（<span lang="EN-US">2</span>）用<span lang="EN-US">lingo</span>求解，将程序附上；<span lang="EN-US"><p></p></span></span></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt;"><span style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体;">（<span lang="EN-US">3</span>）模型不唯一，可用多种方法。<span lang="EN-US"><p></p></span></span></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt;"><span lang="EN-US"><p><font face="Times New Roman">
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