Calc
posted by Martina .
A rectangular storage container with an open top is to have a volume of 15m^3. The length of the base is twice the width of the base. Material for the base costs $6 per square meter. Material for the sides costs $7 per square meter. Find the cost of the materials for the cheapest such container. Round answer to nearest hundredth.
I know that you need to find an equation, get the derivative, find the critical numbers, and then find the minimum. But, I have no clue on how to find the equation! If someone could please help me!
You will need a diagram.
Visualize the box "flattened", you have a rectangular base, with rectangles on each of its sides.
These four rectangles must have the same width, namely the height of the box.
Let that height be h m.
Let the width of the base be x m, then its length is 2x m.
So the volume is x(2x)h or 2hx^2 m^3
but we know this is 15.
So one of the equations is 2hx^2 = 15 or
h = 7.5/x^2
Since you want to minimize the Cost, you now need an equation for Cost
Cost of base = 6(x)(2x)=12x^2
Cost of sides = 2(7)(x)h) + 2(7)(2x)(h)
=42xh
Cost = 12x^2 + 42xh
=12x^2 + 42x(7.5/x^2)
=12x^2 + 315/x
Cost' = 24x  315/x^2 = 0 for a min of Cost
Solve this....i got x=2.3588....
You actually have to plug it into the original cost equation and I get $200.31 and it's the right answer! Thank you so very much for your help!!!!
Respond to this Question
Similar Questions

math (calc)
At noon, ship A is 150 km west of ship B. Ship A is sailing east at 35 km/h and ship B is sailing north at 25 km/h. How fast is the distance between the ships changing at 4:00 pm. Find the intervals of increase or decrease find the … 
Calculus optimization
A rectangular storage container with a lid is to have a volume of 8 m. The length of its base is twice the width. Material for the base costs $4 per m. Material for the sides and lid costs $8 per m. Find the dimensions of the container … 
HELP!! OPTIMIZATION CALCULUS
A rectangular storage container with a lid is to have a volume of 8 m. The length of its base is twice the width. Material for the base costs $4 per m. Material for the sides and lid costs $8 per m. Find the dimensions of the container … 
Calculus
AM having problems understanding what equations to use for this word problem. Please help. A rectangular storage container with an open top is to have a volume of 48ft^3. The length of its base is twice the width. Material for the … 
Calc 1 (Optomization)
A rectangular storage container with an open top is to have a volume of k cubic meters. The length of its base is twice its width. The material for the base costs $6 per square meters and the material for the sides costs $10 per square … 
Calculus
A rectangular storage container with an open top is to have a volume of 10m^3. The length of its base is twice the width. Material for the base costs $3 per m^2. Material for the sides costs $10.8 per m^2. Find the dimensions of the … 
Calculus
A rectangular storage container with an open top is to have a volume of k cubic meters. The length of its base is twice its width. The material for the base costs $6 per square meters and the material for the sides costs $10 per square … 
Calc 1
A rectangular storage container with an open top is to have a volume of 10 m3. The length of the base is twice the width. Material for the base is thicker and costs $13 per square meter and the material for the sides costs $10 per … 
Calculus
A rectangular storage container with an open top is to have a volume of 10 . The length of its base is twice the width. Material for the base costs $12 per square meter. Material for the sides costs $5 per square meter. Find the cost … 
Calculus
A rectangular storage container with an open top is to have a volume of 10 m3. The length of its base is twice the width. Material for the base costs $9 per m2. Material for the sides costs $150 per m2. Find the dimensions of the container …