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 which will minimize cost and the minimum cost. I need the minimum cost , I found the dimensions to length=10
Width=5 height=0.2. Need the cost in $. Thanks!!!
Damon had answered this and 4 others for you, why are you switching names?
I pointed out your error here.
https://www.jiskha.com/display.cgi?id=1511687459
To find the cost in dollars ($), we need to calculate the total cost of the base and sides separately and then add them together.
1. Cost of the Base:
The base of the rectangular container is a rectangle with dimensions length and width. The cost of the base is given as $9 per square meter (m2).
The area of the base (Abase) can be calculated by multiplying the length (L) and width (W):
Abase = L * W
Substituting the given values, we have:
Abase = 10 * 5 = 50 m2
To find the cost of the base, we multiply the area by the cost per square meter:
Cost_base = Abase * Cost_per_m2
Cost_base = 50 * $9 = $450
So, the cost of the base is $450.
2. Cost of the Sides:
The sides of the container form a rectangle with dimensions length, width, and height. The cost of the sides is given as $150 per square meter (m2).
The surface area of the sides (Aside) can be calculated by summing the areas of all four sides:
Aside = 2(L * H) + 2(W * H)
Substituting the given values, we have:
Aside = 2(10 * 0.2) + 2(5 * 0.2)
Aside = 4 + 2 = 6 m2
To find the cost of the sides, we multiply the area by the cost per square meter:
Cost_sides = Aside * Cost_per_m2
Cost_sides = 6 * $150 = $900
So, the cost of the sides is $900.
3. Total Cost:
The total cost is the sum of the cost of the base and the cost of the sides:
Total Cost = Cost_base + Cost_sides
Total Cost = $450 + $900 = $1,350
Therefore, the minimum cost to build the container with the given dimensions is $1,350.