1. Acme, Inc. produces widgets (w) and gadgets (g). Its profit func...

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1. Acme, Inc. produces widgets (w) and gadgets (g). Its profit function is given by: TO = 20w - a) How many widgets and gadgets should Acme sell to maximize profits? b) Suppose there is a constraint on production such that w + g 8. Compute the optimal quantity of widgets and gadgets. 2. A firm has revenue and cost functions given by: R = 1000Q-2Q² C = Q3-59Q² + 1315Q-2000 Show the profit function. Note that the function is "optimized" when Q = 3 and Q = 35. Find the profit maximizing level of output and profits by checking the sign of the second derivative of the profit function with respect to Q. 3. For five years, an oil drilling company has operated profitably in the state of Alaska (the only place it operates). Last year, the state legislature instituted a flat annual tax of $100,000 on any company extracting oil (or natural gas) in Alaska. How would this tax affect the amount of oil the company extracts? Explain. Suppose instead the state imposes a wellhead tax-that is, oil companies must pay a tax of $2.00 on each barrel of oil extracted. How would this tax affect the amount of oil the company extracts? Explain. 4. Suppose you are the manager of a California winery. How would you expect the following events to affect the price for a bottle of wine (assume that you are a "price-taker")? Use demand and supply curves to illustrate. a. The price of comparable French wines decrease. b. The unemployment rate in the United States decreases. c. The price of cheese increases. d. The price of a glass bottle significantly increases due to new government anti-shatter regulations. e. Researchers discover a new wine-making technology that reduces production costs. f. The price of vinegar, which is made from leftover grape mash, increases. g. The average age of consumers decreases, and older people drink less wine. 5. Differentiate the functions defined by the various formulas: b. 12-2x2+5x3 2 1 X c. 1-3x7 - d. x-2(22+1)VE - e. x+1 Xt/ For this function, determine the value(s) of x where dy/dx = 0: f. f(x)==(xx-6x2)

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