Homework Week 5

1. (7 points) Consider the following linear program:
   Minimize A - B
   Subject to:
   -4A + 3B <= 3
   A – B <= 3
   A >= 0
   B >= 0
   1. Graph the feasible region for the problem. (2 points)
   2. Is the feasible region unbounded? Explain. (1 point)
   3. Find the optimal solution (either graphically or using Excel). (2 points)
   4. Does an unbounded feasible region imply that the optimal solution to the linear program will be unbounded? Explain. (2 points)
2. (9 points) The accompanying table shows the index of production in the iron and steel industry for the years 1981 to 1994 , where the index value for 1987 is 100 . Plot the data.
   
   
   1. Estimate the linear trend line. Estimate b0 and b1 . (2 points)
   2. Estimate the quadratic polynomial trend curve. Hint: include the input variable period2 (2 points)
   3. Compare adj. R^2 for both models. Which is better according to adj. R^2? Explain. (1 point)
   4. Which coefficients of the linear model (b0, b1) and quadratic model (b0, b1, b2) are significant at alpha = 0.05? (2 points)
   5. Forecast the values of the index for 1998, 1999 and 2000 by using the linear trend line and the polynomial trend curve. Use the formulas that you determined in parts a and b. (2 points)
3. (10 points) The accompanying data show the money supply (currency plus demand deposits) for the years 1981 to 1994.

1. Estimate the linear trend line using \(t=1\) in 1981 and calculate \(R^{2}\).
2. Estimate the money supply in 1995 and 1996 using the linear trend line.
3. Estimate the equation \(\ln Y_{1}=\beta_{0}+\beta_{1} t+e_{t}\), and calculate \(R^{2}\).
4. Estimate the money supply in 1998 and 1999 using the exponential trend line.
5. Compare adj. R^2 for the two models. Which is better? (1 point)

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