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In the link below, how do I graphically show the profit-maximization point?

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There are two different ways to determine the profit maximizing level of output.

One way is the total revenue minus total costs method.  To show this graphically, you need to subtract total costs from total revenues for each of the nine levels of output given.  This figure is already provided for you for output = 0 and output = 100.   Then make a graph where the vertical axis is the amount of profit in dollars (it will start as a negative number, rise, and then fall) and the horizontal axis is the level of output.  You will find that the curve peaks when the output is 600 kilograms per month and then falls.  That shows that 600 is the profit maximizing output.

The other way is the marginal revenue = marginal costs method.  Here, you must find the marginal revenue for each level of production.  This will be the same at every level and will therefore be a horizontal line.  You then find the marginal costs.  This will be something of a j-shaped curve that goes down at first and then rises.  The point at which they cross is the profit maximizing point because MR=MC at that point.  If you draw it correctly, that point will be at 600 kg/month of production.

You can see examples of such graphs at this link.

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