First you need to create the demand function to relate revenue to the price increase\decrease. To do this you will need to find another point to calculate the slope. I picked the point 22, 390 ($10 decrease 2 bikes sold increase).

Now I calculate the slope (390-400)/(22-20)=-5. Now you can put this into slope intercept form with the original pts. y-400=-5(x-20) sim: y=-5x+300.

Now we can create the primary function. Profit is Revenue - Cost. What is the revenue in this case? It is number of units sold multiplied by price. This is x*y. Y is related to x via the demand function we just created. What is the cost? The cost is a given, and it is $200. However, we must remember to multiply it by the number of units sold; so for the function the cost is 200x.

So the primary function will be P(x)=x*(-5x+300)-200x. sim: -5x^2+100x

Now we can differentiate and solve for zero to find critical values and possible mins and maxes.

-10x+100=0

-10x=-100

x=10

Maximum profit will be made when 10 units are sold. Given our earlier relationship we know that the cost per unit will be $250. The cost will be $2000, so the max profit that can be made is $500.