Exercises 1-24, solve the given LP problem. If no optimal solution exists, indicate whether the feasible region is empty or the objective function is unbounded. [ HINT: See Example 1.] Maximize and Minimize p = 2 x − y Subject to x + y ≥ 2 x − y ≤ 2 x − y ≥ − 2 x ≤ 10 , y ≤ 10 .
Exercises 1-24, solve the given LP problem. If no optimal solution exists, indicate whether the feasible region is empty or the objective function is unbounded. [ HINT: See Example 1.] Maximize and Minimize p = 2 x − y Subject to x + y ≥ 2 x − y ≤ 2 x − y ≥ − 2 x ≤ 10 , y ≤ 10 .
Solution Summary: The author calculates the optimal solution of a linear programming problem to maximize and minimize p=2x-y subject to the given constraints.
Exercises 1-24, solve the given LP problem. If no optimal solution exists, indicate whether the feasible region is empty or the objective function is unbounded. [HINT: See Example 1.]
1. A bicyclist is riding their bike along the Chicago Lakefront Trail. The velocity (in
feet per second) of the bicyclist is recorded below. Use (a) Simpson's Rule, and (b)
the Trapezoidal Rule to estimate the total distance the bicyclist traveled during the
8-second period.
t
0 2
4 6 8
V
10 15
12 10 16
2. Find the midpoint rule approximation for
(a) n = 4
+5
x²dx using n subintervals.
1° 2
(b) n = 8
36
32
28
36
32
28
24
24
20
20
16
16
12
8-
4
1
2
3
4
5
6
12
8
4
1
2
3
4
5
6
=
5 37
A 4 8 0.5
06
9
Consider the following system of equations, Ax=b :
x+2y+3z - w = 2
2x4z2w = 3
-x+6y+17z7w = 0
-9x-2y+13z7w = -14
a. Find the solution to the system. Write it as a parametric equation. You can use a
computer to do the row reduction.
b. What is a geometric description of the solution? Explain how you know.
c. Write the solution in vector form?
d. What is the solution to the homogeneous system, Ax=0?
Chapter 6 Solutions
Finite Mathematics and Application Calculus (Looseleaf) - Text Only
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