Lone Depot and Homes are two competing home improvement stores. Each claims to provide customers with a cost-effective, versatile rectangular storage container with a square base, an open top, and a volume of 36 ft' (see the diagram below). Each company has determined they want to use the same type of materials to construct the containers. The material for the sides and top of each container costs $2/ft2, and the material for the bottom costs $4/ft2. Lone 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 by 2.5 ft by 5.76 ft. However, Homes claims that the minimum cost of producing such a container can be obtained if the dimensions of the container are 4 ft by 4 ft by 2.25 ft.
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
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Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
Given the information in the picture attatched,
Which company's proposed dimensions are better? In other words, which will result in a lower cost of constructing each container? (Explain with math and words)
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