An Open Box with Volume Of $8000$ Cm $3$ Is to Be Constructed by Taking a Piece of Cardboard

question 67

Essay

An open box with volume of $8000$ cm $3$ is to be constructed by taking a piece of cardboard $40$ cm by $60$ cm, cutting squares of side length $x$ cm from each corner. Show that this can be done in two ways, and find the exact dimensions of the box in each case.

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Definitions:

Production Inefficiencies

Situations where resources are not used in the most productive way, leading to wastage and a lower output than potentially achievable.

Technological Breakthrough

A significant advancement in technology that dramatically changes the production process or market for goods and services, often leading to efficiency improvements and new opportunities.

Scarcity

The fundamental economic problem of having seemingly unlimited human wants and needs in a world of limited resources.

Opportunity Cost

Incurring a cost by overlooking the next most advantageous option when making choices.