某电视机厂计划在下一个生产周期内生产两种型号电视机，每台A型或B型电视机所得利润分别为6和4个单位，而生产一台A型或B型电视机所耗原料分别为2和3个单位；所需工时分别为4和2个单位，如果允许使用的原料为100单位，工时为120单位，且A或B型电视和产量分别不低于5台和10台，应当生产每种类型电视机多少台，才能使利润最大？
设生产A型电视机x台，B型电视机y台，则根据已知条件线性约束条件为
，即2x+3y≤100 4x+2y≤120 x≥5 y≥10 2x+3y≤100 2x+y≤60 x≥5 y≥10
线性目标函数为z=6x+4y．
根据约束条件作出可行域如图所示，作3x+2y=0．
当直线l0平移至过点A时，z取最大值，
解方程组
得2x+3y=100 2x+y=60 x=20 y=20
生产两种类型电视机各20台，所获利润最大．
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