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200 mm 20mm 20mm V 210mm 20mm 110mm Figure 2 Determine the maximum shear force (V) the cross section shown in Figure 2 can carry if the maximum shear stress is not to exceed 100MPa. Using the calculated V, determine the force carried by the web 15 F

 

2 If I is an eigenvalue of n x n matrices A and B corresponding to the same eigenvector x then 21 is an eigenvalue of A + B that corresponds to w. O True O False 3

 

The marginal revenue function of a perfect competition producer is me 100 - 69. What is the total revenue function?

I. (Overbooking Problem) An airline is considering an overbooking policy for its flights from LA to Las Vegas to avoid flying with empty seats. During the past month, the no-show experience has been:

No-shows	0	1	2	3	4
Percentage	30	25	20	15	10

 

(a) (8 pts) What would be your recommendation for overbooking if the one-way ticket sells for $100 and the cost of not accommodating a customer due to overbooking is a free gift worth $20 plus a free seat on the next flight (with a full refund for his/her original ticket)? Assume no cancellation fee or penalty to the passengers who do not show up. The marginal cost to serve a customer (e.g., drink) is negligible.

(b) (4 pts) What is the expected loss per flight for your overbooking choice?

 

II. (Capacity Allocation Problem, 8 pts) A ski resort is planning a year-end promotion by offering a weekend special room rate for $199. The high season room rate for these rooms is $299. Management wants to hold some rooms for late arrivals who are willing to pay the season rate. If the weekend demand for the rooms from the skiers who are willing to pay full rate is normally distributed with mean 40 and standard deviation 10, how many rooms should be set aside for full-paying skiers?    

PO Q.2 Homeland has an economy that produces only three final goods: meat, coal, and wheel Information on population, nominal prices and total output for each good in the years 2001 and 2007 is given below. Meat Coal Wheel 2002 2008 per unit Price (S) Output (in millions) per unit Price (S) Output (in millions) 3.00 2 5.00 5 4.50 5 7.00 8 2.50 8 3.00 10 Note: The population of Homelands for years 2002 and 2008 are 15,000 and 20,000, respectively. a) Calculate nominal GDP for 2002. b) Calculate nominal GDP for 2008. c) Calculate real GDP for 2002 and 2008 if the BASE YEAR is 2002. d) Calculate the growth rate of real GDP (using 2002 S). e) Has the standard of living increased or decreased since 2002? 1) Calculate real GDP for 2002 and 2008 if the BASE YEAR is 2008. g) Calculate the growth rate of real GDP (using 2008 $). h) What is the GDP deflator for 2002 and for 2008? (Use 2002 as the base year.) i) What is the GDP deflator for 2002 and for 2008? (Use 2008 as the base year.) j) By what percent has the price level increased between 2002 and 2008? (Use GDP deflators with base year 2002).

2: If X is a random variable that is uniformly distributed on (0,1), and Y is an independent) exponential random variable with paramter, please find the p.d.f. of Z:=Y - X.

 

I need 2(ii) solutions

= - - 2. Consider the following PDE ?? 2²T at Ox² The initial and boundary conditions are T(0,x)=sin(x) T(t,0)=0, T(1,1)=0. i) Use the explicit method to solve the equation at t = 0.1s with step sizes Ar = 0.2 cm and At = 0.05 ii) Use the simple implicit method to generate the tridiagonal system of equations for heat distribution at t = 0.05 s with step sizes Ar = 0.2 cm and t = 0.05. Solve the generated system using the Gauss-Seidel method with the initial guess, 10) = 0. Compute the numerical solutions for the first 2 iterations. 111) Use the Crank-Nicolson method to generate the tridiagonal system of equations for heat distribution at t = 0.05 s with step sizes Ar = 0.2 cm and t = 0.05. Solve the generated system using the Gauss-Seidel method with the initial guess, T0 = 0). Compute the numerical solutions for the first 2 iterations. - = = - - - =

QUESTION 3 S 200mm S 30 mm 30 mm 300 mm 30 mm Figure 3 The beam shown is made up of three individual members. If a 500N load is applied and the shear stress in each nail is not to exceed 100MPa (the nail diameter is 5mm) determine the spacing distance “S” of the nails.