An open box is to be made by cutting congruent squares from each corner of a 20cm by 30cm rectangular piece of cardboard.
What are the conditions on the HEIGHT of the box?
Draw and appropriately label a NET for the box if its height is arbitrary (h cm)
Write an equation for the VOLUME of this box if its height is h
Determine the volume when h = 4cm, & when h = 9cm, & h = 12cm
What dimensions will maximize the volume of a box made from this material?
What will the maximum volume be?
Use an online resource or app to create a valid, properly scaled and labeled graphic model for this investigation. Label applicable points.
Practice creating & investigating the same version of the graph on your calculator.
2. The COST FUNCTION (what the owner pays for upkeep, supplies, etc) for a certain business is given by C(x) = 200+10x+0.2x2, where x = # items produced.
The REVENUE FUNCTION (amount from the sale of items) is given by
R(x) = 40x-0.1x2, where x = # items sold
When is the REVENUE greater than the cost? And what does this indicate about the status of the business with respect to this item?
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