D: P=100-Q and S: MC=Q. What is the profit-maximizing price and quantity? Round to two decimal places as you work and for your final answer. Please show all steps.

The value of marginal revenue is $35 and the value of marginal cost is $30 Is the firm maximizing profits?

①The total cost for producing x items is given by 12x + 3735. Each item is sold for $21. Find the formula for the total items must be sold to break even? revenue. How Many ②Solve the equation x² - 10x = -2x-15 3 A department store will buy 8 items if the price is $40 per item, and 14 items if the price is $28 per item. The Supplier is willing to sell 5 items if the price is $70 per item and 12 items if the price is $140 per item. If the supply and demand functions are linear, find the equilibrium point. invest $10,000 in an account that pays 10% compounded you continuously, how much money will you have in 15 years? (4) If ⑤ het f(x) = 300 √x + 2. Find the average rate of change when x increases from 25 to 100. Calculate derivatives of the following functions. a) 2 2x-3 4x+5 b) (2x5 +1) 9 ⑦Calculate derivatives of the following functions 8 の 2 6x в) че 6) 1) In (3x² + 5x) Calculate the following integral S (8x7 - 12x 5 + 3x² + 4) dx

Suppose that over the short run (say the next 5 years), demand for OPEC oil is given by   P = 165 – 2.5q. Here q is measured in millions of barrels a day. OPEC marginal cost per barrel is $15.   What is OPEC’s optimal level of production? What is the prevailing price of oil at that level? Many experts contend that maximizing short-run profit is counterproductive for OPEC in the long run because high price reduces buyers to conserve energy and spur competition and new exploration that increases the overall supply of oil. Suppose that the demand curve just described will remain unchanged only if oil prices stabilize at $65 per barrel or below. If oil price exceeds this threshold, long run demand (over a second five year-period) will be curtailed to P = 135 – 2.5q. OPEC seeks to maximize its total profit over the next decade. What is the optimum output and price policy? (assume all values are present values)