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BUS-301 MBA Managerial Econ class assignment -3, Q1Suppose a firm sells two products labeled: x & y.

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Question;Assignment #3;1.;Suppose a firm sells two;products labeled: x & y. The total revenue function for these products is;TR = 36x ? 3x2 + 40y ? 5y2. And the total cost function;is: TC = x2 + 2xy + 3y2. Find;a.;The optimal levels of x & y;this form should produce to maximize profits.;b.;Be sure to check and show the;second order conditions confirming your results.;c.;What are the prices of both;goods x & y at the optimal levels?;2.;Suppose a firm has a cost;function: TC = 4x2 + 10y2. The production manager want to know the;quantities of each product that will minimize the total cost if the total;output of x & y must equal 800.;a.;Solve this problem for the;manger using the Lagrangian method.;b.;How would this manager use the;resulting Lagrangian multiplier in this case?;3.;The supply function for a;particular kind of cheese is: Qs = 100 + 3P where Qs is the quantity supplied;of this cheese in millions of pound per year, and P is the price of this cheese;in dollars per pound. If the demand function is: Qd = 106 million pound of;cheese per year and if the government imposes a price floor of $1 per pound;a.;Will there be excess supply or;excess demand for this cheese? How big will it be?;b.;What if the government sets a;price floor of $3 per pound? Will there be excess demand or supply? How big;will it be?;4.;Given the following Demand and;Supply functions for wheat in the U.S.;Qd = 3.1 ? 0.25P;Qs = 1.3 + 0.5P;Find;a.;Equilibrium price and quantity.;b.;Price elasticity of demand at;equilibrium.;c.;If wheat prices increased slightly;would we expect total revenues to increase or decrease? Explain using the;elasticity coefficient you calculated above.;5.;The B-2 bomber was designed as;a stealthy long range bomber. Two Northrop engineers used mathematical analysis;to determine how an aircraft?s volume should be proportioned between the wing;and the fuselage to maximize its flying range. Taking the derivative of range;with respect to volume, they found that this derivative equaled zero when the;total volume was almost all wing. Hence the result was the flying wing;configuration. Thus the engineers concluded that this configuration would;maximize the flight range. However, in reality, this aircraft exhibits one of;the worst flying ranges in the Air Force inventory. There was a flaw in the;engineers? analysis. What was it?;6. Given;the following demand functions;x;= 25 ? 0.5 Px;y;= 30 ? Py;with the combined cost function: c = x2 +;2xy + y2 + 20;Find;The profit;maximizing output for each product.;Price of each;product.;Profit.

 

Paper#52084 | Written in 18-Jul-2015

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