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- Consumers' Surplus The demand function for a certain brand of mattress is given by P = 300e where p is the unit price in dollars and x (in units of a hundred) is the quantity demanded per month. (a) Find the number of mattresses demanded per month if the unit price is set at $200/mattress. (Round your answer to the nearest integer.) 1352 mattresses -0.03x (b) Use the results of part (a) to find the consumers' surplus if the selling price is set at $200 per mattress. (Round your answer to the nearest dollar.) $The price-demand equation, D(x), and the price-supply equation, S(x), of a Slow Cooker are given below. k - x p = D(x) = and p =s(x) = 0.25x2 + 7, for some constant k. 4 %3D When the price is pegged at $15, the consumers' surplus is found to be $200. (a) Find k. (You will be able to solve for two values of k. Provide an explanation why one of these values is not feasible.) (b) Find the equilibrium price and equilibrium quantity using the value of k found in part (a). (c) Find the consumers' surplus at the equilibrium point. Interpret what this value represents. (d) Find the producers' surplus at the equilibrium point. Interpret what this value represents.Mead Plumbing currently sells thread seal tape at a price of $42.00 per roll. Their research department has derived the price-demand equation as p = 60 -0.02x where x is the number of tapes that can be sold at $p per roll of tape. (d) If the current price changes by 10%, what will be the approximate percentage change in demand? (e) Find the price at which a percentage change in price produces the same percentage change in demand.
- Suppose the demand function for a product is given by the function: D(q) = -0.014g + 54.6 Find the Consumer's Surplus corresponding to q = 1,400 units. (Do no rounding of results until the very end of your calculations. At that point, round to the nearest tenth, if necessary. It may help you to sketch the demand curve, which crosses the horizontal at q = 3,900.) Answer: dollarsPlease no written by hand the demand function for a manufacturer's product is p = f(g) = - 0.20g + 500, where p is the price (in dollars) per unit when q units are demanded (per day). Find the level of production that maximizes the manufacturer's total revenue and determine this revenue. what quantity will maximize the revenue. q = blank unitsect of the utility commission's ruling on the profitability of the firm? 15 A company estimates that the demand for its product fluctuates with the price it charges. The demand function is q = 280,000 – 400p where q equals the number of units demanded and p equals the price in dollars. The total cost of producing q units of the product is estimated by the function C = 350,000 + 300q + 0.0015q? (a) Determine how many units q should be produçed in order to maximize annual profit. (b) What price should be charged? (c) What is the annual profit expected to equal? 16 Solve the previous exercise, using the
- The price p (in dollars) and the quantity q sold of a certain product obey the demand equation q = 800–20p and 0< p< 40 (i) Express the revenue R as a function of q. (ii) What is the revenue if 20 units are sold?The demand function for an item is given by d(x) = 100/ 0.01x 2 + 1 (20 ≤ x ≤ 50) where d(x) (measured in units of a thousand) is the quantity demanded per weak and x is the unit price in dollars. (a) Find the rate of change in demand with respect to price. (b) How fast is the demand changing at price equal to 30 (x = 30)?a) The demand function for a product is p = 60 3-9/15) where q is the number of units and p is the price of one unit. At what price will the demand be 15 units? How many units will be demanded if the price is $41.60?
- The demand function for a certain kind of laptop is given by -0.04x p = 600e where p is the unit price in dollars and x (in units of a hundred) is the quantity demanded each month. (a) Find the number of laptops demanded per month of the unit price is set at $500 per laptop. (b) Use the results of part (a) to find the consumers' surplus if the selling price is set at $500 per laptop.It is known that the quantity demanded of a certain make of portable hair dryer is x hundred units/week and the corresponding wholesale unit price is p = sqrt of 289 - 3x dollars. Determine the consumers' surplus if the market price is set at $14/unit. (Round your answer to two decimal places.) $a) A supply function indicates the number of units of a commodity that suppliers are willing to bring to the market place as a function of price consumers are willing to pay. The function is qs = 0.5p2 – 200, determine the following: i: What class of function is this?ii: What quantity can be supplied if the market price is Rs. 30 & Rs. 50?iii: What price would result in 0 unit being brought to the market place?