1、
長寬為x、y,則2(x+y)=36,x+y=18
S = xy ≤ (x+y)²/4 = 81
當(dāng)且僅當(dāng) x = y = 9時(shí),等號成立
∴長寬都為9
2、
設(shè)房屋另外兩棱(即：長寬,這樣設(shè)不用討論)分別為x、y (m) ,總造價(jià)為p (元)
則xy = 12
p = 1200×3x + 2×800×3y + 5800
=3600x + 4800y + 5800
=1200(3x+4y)+5800
≥1200×2√(3x×4y) + 5800
= 1200×2√(12×12) + 5800
=28800 + 5800
=34600
當(dāng)且僅當(dāng)3x = 4y ,即x = 4,y = 3時(shí),等號成立.
∴長為4m,寬為3m,最低造價(jià)為34600元.
3、
設(shè)與墻平行的邊為x(m),與墻垂直的邊為y(m)
則x+2y = 30
S = xy
= (1/2)·x·(2y)
≤(1/2)(x+2y)²/4
=112.5
當(dāng)且僅當(dāng)x = 2y = 15,y=7.5時(shí),等號成立
∴長寬分別為15m,7.5m,最大面積為112.5m²
4、(你確定這題是求最小值?)
∵x＜0,∴-x＞0
∴y=9x+4/x = - [(-9x) + 4/(-x)] ≤ - 2√[(-9x) × 4/(-x)] = -12
最大值為 -12