Question

7. (5 points) A rectangular storage container storage container with an open top is to have a volume of 10 m. The length of its base is twice the width. Material for the base costs $10 per square meter. Material for the sides st $6 per square meter. Find the cost of materials for the cheapest such container. Note: If we let 1, b denote the length and breadth of the base and let h denote the height, then the volume of the box is lbh, which is required to be 10m”.

solve with step please :)

Answer 1

Ginan a box (cuboid) of a fixed olume we need to find such box whose susface area should be minimum for cost of materials to be minimum. dength se breadth she height h l=26 lbh=10 = 26²4=10 Area of base = lb =26? Cоѕt іх бок = 10xus 25- Area of sides f ace th) h L =2 (ab tb) h = obh. I cost for sides - 6x:6bh =36bh - = h = 5/12 Total cost = 206² +36bh bhana wb? +36 6.5 to CCD = 2012 t 180 lo for minimum cost de zo I db de caob -180 =0.08 db =) 263 -9= 0 = b ött . : D ba lv 651 Cost = CCD =cC1.650 = 20 (1.6510² +120 1.651 =163.544 CSScanned with CamScanner