✔ 最佳答案
(1) 4500/x = 可以整除的情形F(x) = (3000/x)*(4500/x) + 0.3x = 13.5*10^6/x^2 + 0.3xF(x)*x^2 = 0.3x^3 + 13.5*10^6兩邊微分並令F'(x)=0:2x*F + 0*x^2 = 0.9x^20.9x = 2F(x) = 2*(13.5*10^6/x^2 + 0.3x)0.3x = 27*10^6/x^2x^3 = 27*10^6/0.3 = 90*10^6x = 100*(90)^(1/3) = 448.14
min = f(448.14) = 201.6632 (2) 4500/x = 不能整除的情形G(x) = (3000/x)*(4500/x + 1) + 0.3x G(x)*x^2 = 3000*(4500 + x) + 0.3x^3
兩邊微分並令G'(x)=0:2xG = 3000 + 0.9x^20 = 3000 + 0.9x^2 - 2[3000*(4500+x) + 0.3x^3]/x= 0.9x^3 + 3000x - 6000*4500 - 6000x - 0.6x^3= 0.3x^3 -3000x - 27*10^6x = 455.578
min = G(455.578) = 208.3026 (3) 兩者合併考慮F(448.14) < G(455.578)所以取 x = 448.14 = Answer
2015-07-25 08:55:32 補充:
繼續:
但是 4500/448.14 = 不能整除
改用最接近數 = 450
所以 Answer: x = 450
min = F(450) = 201 + 2/3