P= 10,000-2Q C = 16,000+ 1648Q +0.4Q² a. Determine the quantity (Q) that maximizes profit. b. Calculate P, R, C, AC, and at the optimal quantity found in part a. c. Determine the quantity (Q) that maximizes total revenue. d. Calculate P, R, C, AC, and at the optimal quantity found in part c. e. Determine the quantity (Q) that minimizes average cost. f. Calculate P, R, C, AC, and x at the optimal quantity found in part e. Equations: Rules for Optimization Profit Maximization MR = MC Revenue Maximization MR 0 Average Cost Minimization MC = AC or Shortcut: for C= a +bQ+cQ² II=R-C R =P* Q AC = C/O Q = (a/c)1/2

Suppose demand is given by p = 1600 − x. Find the maximum revenue.

A firm produces headphones in two qualities, Basic (B) and Premium (P). For the coming year, the estimated quantity produced of B is 60% higher than that of P. The firm makes a markup of 170% on both products. The ratio between the profits per unit between P and B is 2. The cost price for P is $260. If the profit target is $115 362 over the next year, how much of each of the two qualities must be produced and what are the two selling prices? (Round the quantities to the nearest unit and the prices to 2 digits after the decimal point if needed) Quantity of B = Answer units Quantity of P = Answer units Selling price of B = Answer $ Selling price of P = Answer $

7. Find the price per unit p that produces the maximum profit given C 2500-75x +0.04x? ar p%3D2000-0.6x? Use P xp-C