Given the picture attached, Determine whether either of these company's dimensions are the best. In other words, determine the dimensions that would MINIMIZE the cost of producing each storage container, as well as the minimum cost. (Solve with math & explain with words please) ^ can you help me solve this problem? Lone Depot and Homes are two competing home improvement stores. Each claims to provide customers with acost-effective, versatile rectangular storage container with a square base, an open top, and a volume of 36 ft' (seethe diagram below).Each company has determined they want to use the same type of materials to constructthe containers. The material for the sides and top of each container costs $2/ft2, and thematerial for the bottom costs $4/ft2.yLone Depot claims that the minimum cost of producing such a container with the de-sired volume of 36 ft can be obtained if the dimensions of the container are 2.5 ft by2.5 ft by 5.76 ft. However, Homes claims that the minimum cost of producing such acontainer can be obtained if the dimensions of the container are 4 ft by 4 ft by 2.25 ft.

Name: Given the picture attached, Determine whether either of these company'
Uploaded: 2024-03-20T07:07:26.000Z
Channel: Bartleby
Description: Given the picture attached, Determine whether either of these company's dimensions are the best. In other words, determine the dimensions that would MINIMIZE the cost of producing each storage container, as well as the minimum cost. (Solve with math

Notice that the container has square base with length x ft. The height of the container is y ft. The container is open in top.The area of the square in the base of the container with length x ft is: x2 ft2 The area of the rectangle in the side of the container with height y ft and width x ft is: xy ft2 Since there are four sides in the container, the total area is: 4xy ft2 Since top of the container is open, it is not necessary calculate the area of the square in the top.The cost for making sides the container is: $2 per 1 ft2 The total area of the square in the sides of the container is 4xy ft2. The cost for sides of the container is: $2(4xy)=$8xy The costs for making bottom of the container is: $4 per 1 ft2 The are of the square in the bottom of the container is x2 ft2. The cost for bottom of the container is" $4x2 The total cost T to make the container is: T=$8xy+4x2 The claim of Lone Depot for the dimension of the container in order to get minimum cost is: 2.5 ft by 2.5 ft by 5.76 ft 2.5 ft represents the length of the base square and 5.76 ft represents the height of the container. Substitute the values in cost function: T=$8xy+4x2=$ 8(2.5)(5.76)+4(2.5)2 =$115.2+25=$140.2The claim of Homes for the dimension of the container in order to get minimum cost is: 4 ft by 4 ft by 2.25 ft 4 ft represents the length of the base square and 2.25 ft represents the height of the container. Substitute the values in cost function: T=$8xy+4x2=$ 8(4)(2.25)+4(4)2 =$72+64=$136The cost for the company Lone Depot if they make the container in the proposed dimension is: T=$140.2 The cost for the company Homes if they make the container in the proposed dimension is: T=$136 The company Homes' claim gives the minimum cost to make the container.