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.

  • HW4-dgfmsj.zip