Question

A tank with rectangular base and rectangular sides open at the top is to be constructed so that its depth is 3 m and volume is 75 m3. If building of tank costs Rs. 100 per square metre for the base and Rs. 50 per square metres for the sides, find the cost of least expensive tank.``

Answer 1

Volume=lbh=75`m^3`
`=lb*3=75`
`=lb=25-(1)`
Cost`=100*l*b+50(l*h+b*h+l*h*b*h)`
`=100lb+100(l+b)h`
cost=`2500+300(l+b)`
Minimize`(2500+300)l+b)`
cost`=2500+300(25/b+b)`
Cost is minimum when`d/db(cost)=0`
`0+300(25(-1/b^2)+1)=0`
`300(1-25/b^2)=0`
`1-25/b^2=0`
`b=sqrt25=5`
`l=25/5=5`
Cost=2500+300(5+5)=2500+3000=5500.