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.
(a) Plot the feasible solution space in the x − y plane.
(b) Solve the optimization problem by using the graphical method.
2. 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.
3. 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.
4. 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
.
