Producer equilibrium is achieved where the isocost line is tangent to the isoquant curve. The isoquant curve shows the different combinations of inputs that produce the same output level, while the isocost line connects combinations that can be purchased with the available budget. Profit is maximized using two methods - where the slopes of the isoquant and isocost lines are equal, or where marginal revenue equals marginal cost at the output level where the total revenue curve's slope equals the total cost curve's slope.