# PreCalculus Homework

**Question description**

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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