Suppose that a firm operates in a competitive market where the commodity price is $15 per unit. The firm's cost equation is C=25+0.25Q^2, where C= total cost and Q= quantity. (a) find the profit maximizing level of output for the firm. Determine its level of profit. (b) Suppose that a fixed costs increase to $75. Verify that this change in fixed costs does not affect the firm's optimal output.