MAE 3210 Homework 4 Solved

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For this homework you are welcome to solve problem 1 by hand, without using programming or submitting code. However, you are required to solve problems 3-4 with programming, and a copy of your code must be submitted. Use of MS excel (or equivalent software) is acceptable and encouraged for problem 2; please include a copy of your final spreadsheet within your submitted PDF.

  1. Consider the optimization problem:

Maximize f(x,y) = −3x + y

subject to the constraints x2 + y ≤ 4,

−2x + y ≤ 0, x ≥ 0.5, y ≥ 0.

  • Plot the feasible solution space in the x y
  • Solve the optimization problem by using the graphical method.
  1. An aerospace company is developing a new fuel additive for commercial airliners.The additive is composed of three ingredients: X, Y , and Z. For peak performance, the total amount of additive must be at least 6 mL/L of fuel. For safety reasons, the sum of the highly flammable Y and Z ingredients must not exceed 2.5 mL/L. In addition, for the additive to work, the amount of Z must be greater than or equal to twice the amount of Y , and the amount of X must be greater than or equal to three quarters of the amount of Y . If the cost per mL for the ingredients X, Y and Z is 20 cents, 3 cents, and 5 cents, respectively, use MS excel to determine the minimum cost of the additive mixture for each liter of fuel.
  2. Use least squares regression to fit a straight line to the data
x 0 2 4 6 9 11 12 15 17 19
y 5 6 7 6 9 8 7 10 12 12

Along with the slope and intercept, compute the standard error of the estimate and the correlation coefficient. Plot that data and the regression line.

  1. The following data are provided
x 1 2 3 4 5
y 2.2 2.8 3.6 4.5 5.5

Perform least squares regression to fit these data to the following model


Note that this problem was solved in class, but here you are asked to reproduce the result on your own.