设该商品定价为x元时,则获得利润为y元
涨价一元,根据题意得:y = (x-40)·〔300-10(x-60)〕
=-10x²+1300x-36000
=-10(x-65)²+6250
300-10(x-60)≥ 0
x≤ 90
当x=65时,函数有最大值6250.
(40≤x ≤ 90)
降价一元,根据题意得:y =(x-40)·〔300+20(60-x)〕
= -20(x-57.5)²+6125,
当x=57.5时,函数有最大值6125
即该商品定价65元时,可获得最大利润.
设该商品定价为x元时,则获得利润为y元
涨价一元,根据题意得:y = (x-40)·〔300-10(x-60)〕
=-10x²+1300x-36000
=-10(x-65)²+6250
300-10(x-60)≥ 0
x≤ 90
当x=65时,函数有最大值6250.
(40≤x ≤ 90)
降价一元,根据题意得:y =(x-40)·〔300+20(60-x)〕
= -20(x-57.5)²+6125,
当x=57.5时,函数有最大值6125
即该商品定价65元时,可获得最大利润.