The quantity demanded of a hand-woven rug is 3000 per month, when the unit price is $500. For each decrease in the unit price of $40, the quantity demanded increases by 200 units. When the price is $100 or fewer sellers are not willing to sell any hand-woven rugs, but at a price of $750 they are willing to sell as much as 4550 hand-woven rugs per month. If the demand and supply functions are assumed to be linear. i. Find the demand function. ii. Find the supply function. iii. Find the approximate equilibrium quantity and price.

need comprehensive and correct answers.This question is about optimization.

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 $