Edlyn makes Special Vegan Cakes to sell at the local street market for fundraising. As Edlyn produces a greater number of Special Vegan Cakes she can lower the price per unit. The function k()=2x -100 relates the price k to the number produced x. The cost c of making x Special Vegan Cakes can be represented with the function c(x) = -10x + 500.
How many Special Vegan Cakes should Teresa sell each week to maximize her profit P?

What is the R(x) or revenue?
What is the P(x) or profit?
How many cupcakes should Teresa sell each week to maximize the profit?
Is there a profit? Explain your reasoning.