Carolina Textiles, Inc., is a small manufacturer of cotton linen that it sells in a perfectly competitive market. Given $100,000 in fixed costs per day, the daily total cost function for this product is described by:

TC = $100,000 + $2Q + $0.0625Q²

MC = dTC/dQ = 2 + .125Q

where Q is units of cotton linen produced per day. Assume that MC > AVC at every point along the firm's marginal cost curve, and that total costs include a normal profit.

Derive the firm's supply curve (supply equation), expressing quantity as a function of price (remember that P = MR in a perfectly competitive market).

Develop the firm's total variable cost (TVC) and average variable cost (AVC) equations?