For a certain civil engineering system, it is sought to maximize the benefits, which is given by the expression: Z=3x+5y. The decision variables are x (the amount of resource type 1 to be used) and y (the amount of resource type 2 to be used). The amount of resource type 1 should be at least 3 units. The amount of resource type 2 should be at least 3 units. The difference between the amount of resource type 2 and the amount resource type 1 should not exceed 6. ▶ The total amount of resource types 1 and 2 should not exceed 12 units. a. Identify the obiective function for this problem. D. Identify and write the constraints. c. Provide a sketch graph for the constraint set. Clearly show the feasible region
For a certain civil engineering system, it is sought to maximize the benefits, which is given by the expression: Z=3x+5y. The decision variables are x (the amount of resource type 1 to be used) and y (the amount of resource type 2 to be used). The amount of resource type 1 should be at least 3 units. The amount of resource type 2 should be at least 3 units. The difference between the amount of resource type 2 and the amount resource type 1 should not exceed 6. ▶ The total amount of resource types 1 and 2 should not exceed 12 units. a. Identify the obiective function for this problem. D. Identify and write the constraints. c. Provide a sketch graph for the constraint set. Clearly show the feasible region
Sustainable Energy
2nd Edition
ISBN:9781337551663
Author:DUNLAP, Richard A.
Publisher:DUNLAP, Richard A.
Chapter2: Past, Present, And Future World Energy Use
Section: Chapter Questions
Problem 2P: A quantity has a doubling time of 110 years. Estimate the annual percent increase in the quantity.
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Transcribed Image Text:For a certain civil engineering system, it is
sought to maximize the benefits, which is given
by the expression: Z=3x+5y.
The decision variables are x (the amount of
resource type 1 to be used) and y (the amount of
resource type 2 to be used).
• The amount of resource type 1 should be at
least 3 units.
• The amount of resource type 2 should be at
least 3 units.
The difference between the amount of
●
resource type 2 and the amount resource type
1 should not exceed 6.
• The total amount of resource types 1 and 2
should not exceed 12 units.
a. Identify the obiective function for this
problem.
b. Identify and write the constraints.
c. Provide a sketch graph for the constraint
set.
d. Clearly show the feasible region.
e. Label all extreme points (or vertices) of the
feasible region and indicate their coordinates.
f. Solve the optimization problem.
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