小明大学毕业回家乡创业,第一期培植盆景与花卉各50盆售后统计,

小明大学毕业回家乡创业,第一期培植盆景与花卉各50盆售后统计,盆景的平均每盆利润是160元,花卉的平均每盆利润是19元,调研发现:

①盆景每增加1盆,盆景的平均每盆利润减少2元;每减少1盆,盆景的平均每盆利润增加2元;

②花卉的平均每盆利润始终不变.

小明计划第二期培植盆景与花卉共100盆,设培植的盆景比第一期增加x盆,第二期盆景与花卉售完后的利润分别为W1,W2.(单位:元)

(1)用含x的代数式分别表示W1,W2

(2)当x取何值时,第二期培植的盆景与花卉售完后获得的总利润W最大,最大总利润是多少?

答案

解:(1)第二期培植的盆景比第一期增加x盆,则第二期培植盆景(50+x)盆,花卉[100-(50+x)]=(50-x)盆,由题意,得

W1=(50+x)(160-2x)=-2x2+60x+8 000,

W2=19(50-x)=-19x+950.

(2)W=W1+W2=-2x2+60x+8 000+(-19x+950)=-2x2+41x+8 950.

∵-2<0,=10.25,x为整数,

∴当x=10时,W最大,

W最大=-2×102+41×10+8 950=9 160(元).

 

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