Given the following linear optimization problem
Maximize 10x + 20y
Subject to
x + y < 50
2x + 3y < 120
x > 10
x, y > 0
(a) Graph the constraints and determine the feasible region.
(b) Find the coordinates of each corner point of the feasible
region.
(c) Determine the optimal solution and optimal objective
function value.
Questions 1 relate to the following constrained optimization
problem: maximize z(x,y)=4x^2-2xy+6y^2 subject to x+y=72. subject
to . A) What is the optimal value of X?
B) What is the optimal value of Y?
C) What is the maximized value of Z?
Consider the following linear programming problem:
Maximize 16X + 14Y
Subject to: 3X + 4Y ≤ 520
3X + 2Y ≤ 320
all variable ≥ 0
The maximum possible value for the objective function is
Consider the following linear programming problem
Maximize 6x1 + 4x2 + 5x3
Subject to:
2x1 + 3x2 + x3 ≥ 30
2x1 + x2 + x3 ≤ 50
4x1 + 2x2 + 3x3 ≤ 120
x1, x2, x3 ≥ 0
a) Find the optimal solution by using simplex method
b) Find the dual price for the first constraint.
c) Find the dual price for the second constraint.
d) Find the dual price for the third constraint.
e) Suppose the right-hand...
Consider the following linear programming problem
Maximize
$4X1 + $5X2
Subject To
2X1 + 5X2 ≤ 40 hr
Constraint A
3X1 + 3X2 ≤ 30 hr
Constraint B
X1, X2 ≥ 0
Constraint C
if A and B are the two binding constraints.
(Round to ONLY two digits after decimal
points)
a) What is the range of optimality of
the objective function?
Answer ≤ C1/C2 ≤ Answer
b) Suppose that the unit revenues for X1 and X2 are changed to
$100 and...
Consider the following linear programming problem
Maximize
$4X1 + $5X2
Subject To
2X1 + 5X2 ≤ 40 hr
Constraint A
3X1 + 3X2 ≤ 30 hr
Constraint B
X1, X2 ≥ 0
Constraint C
if A and B are the two binding constraints.
(Round to ONLY two digits after decimal
points)
a) What is the range of optimality of
the objective function?
.......... ≤
C1/C2 ≤ ............
b) Suppose that the unit revenues for X1 and X2 are changed to
$100 and...
The objective of a linear programming problem is to
maximize 1.50A + 1.50B, subject to 3A + 2B ≤ 600, 2A + 4B ≤ 600, 1A
+ 3B ≤ 420, and A,B ≥ 0. Using Lingo software determine the optimal
product mix for this problem? (include Lingo output)
Please use excel! Thanks!