Suppose that for a certain company, C(x)=35x+1500 represents the total cost function, and R(x)=60x represents the total revenue function. (a) Find the total-profit function (b) Find the break -even point. (a) The total-profit function is P(x)= (Type your answer in slope-intercept form.)

(a) The total-profit function is the difference between the total revenue function and the total cost function. So, we subtract the cost function from the revenue function to get the profit function. <br /><br />\[P(x) = R(x) - C(x) = 60x - (35x + 1500) = 25x - 1500\]<br /><br />(b) The break-even point is when the total cost equals the total revenue, i.e., when the profit is zero. So, we set the profit function equal to zero and solve for x.<br /><br />\[0 = 25x - 1500\]<br /><br />Solving for x gives us the break-even point.