## Description

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.

- Consider the optimization problem:

Maximize *f*(*x,y*) = ā3*x *+ *y*

subject to the constraints *x*^{2 }+ *y *ā¤ 4*,*

ā2*x *+ *y *ā¤ 0*, x *ā„ 0*.*5*, y *ā„ 0*.*

- Plot the feasible solution space in the
*x*ā*y* - Solve the optimization problem by using the graphical method.

- 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. - 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.

- 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.