5. In optimization problems with equality constraints: a) the number of constraints equals the number of...
5. In optimization problems with equality constraints: a) the number of constraints equals the number of choice variables. b) the number of constraints may equal the number of choice variables. c) the number of constraints must exceed the number of choice variables. d) the number of constraints may exceed the number of choice variables. e) the number of constraints must be smaller than the number of choice variables.
Homework Answers
a) the number of constraints equals the number of choice variables
Equality constraint removes one degree of freedom. So it is necessary to have number of constraints equals variables.
In optimization problems with inequality constraints, the number of constraints is greater than variables.
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5. In optimization problems with equality constraints: a) the
number of constraints equals the number of...
9. In optimization problems with inequality constraints, the value of the Lagrange function, in an optimum:...
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Formulate the followings into optimization problems. While you could use the integer constraints, the linear structure...
Formulate the followings into
optimization problems. While you could use the integer constraints,
the linear structure should be maintained. However, you shouldn’t
use the integer constraints if you can formulate the problem
without them. Describe the decision variables, objective function
and constraints carefully. You don’t need to solve this
problem.
(b) (10 pts) Three workers are available to perform two jobs. The timei takes each worker to perform each job is given in the following table. Formulate the problem to...
Formulate the followings into optimization problems. While you could use the integer constraints, the linear structure should be maintained. However, you shouldn’t use the integer constraints if you c...
Formulate the followings into optimization problems. While you
could use the integer constraints, the linear structure should be
maintained. However, you shouldn’t use the integer constraints if
you can formulate the problem without them. Describe the decision
variables, objective function and constraints carefully. You don’t
need to solve this problem.
(b) (5 pts) A KAIST student is planning a back-pack trip to Europe for this summer. There are 11 items (1 through n) that she is considering to carry to...
a) Formulate a cost function along with constraints, if any, for the following optimization problems. You don't nee...
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a) Formulate a cost function along with constraints, if any, for the following optimization problems. You don't nee...
a) Formulate a cost function along with constraints, if any, for the following optimization problems. You don't need to solve any of these problems. i) Two electric generators are interconnected to provide total power to meet the load. Suppose each generator's cost (C) is a function of its power output P (in terms of units), and costs per unit are given by: C2 = 1 + 0.6P2 + P22 (for Generator 2). -1-P -Pi2 (for Generator 1), If the total...
please help me the best you can Part 1: Optimization with inequality constraints 1. A consumer...
please help me the best you can
Part 1: Optimization with inequality constraints 1. A consumer lives on an island. Her utility function is U = (x²y)1/3. She produces two goods, x and y. She faces a production constraint and an environmental constraint: Her production possibility frontier is: x² + y2 s 300. She faces an environmental constraint given by x + y = 200. a) Set up the Lagrangian function. b) List all of the Kuhn-Tucker conditions. c) Interpret...
_________________ are mathematical problems defined as a set of objects whose state must satisfy a number...
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Formulate the followings into
optimization problems. While you could use the integer constraints,
the linear structure should be maintained. However, you shouldn’t
use the integer constraints if you can formulate the problem
without them. Describe the decision variables, objective function
and constraints carefully. You don’t need to solve this
problem.
(b) (10 pts) Three workers are available to perform two jobs. The timei takes each worker to perform each job is given in the following table. Formulate the problem to...
Formulate the followings into optimization problems. While you
could use the integer constraints, the linear structure should be
maintained. However, you shouldn’t use the integer constraints if
you can formulate the problem without them. Describe the decision
variables, objective function and constraints carefully. You don’t
need to solve this problem.
(b) (5 pts) A KAIST student is planning a back-pack trip to Europe for this summer. There are 11 items (1 through n) that she is considering to carry to...
a) Formulate a cost function along with constraints, if any, for the following optimization problems. You don't need to solve any of these problems i) Two electric generators are interconnected to provide total power to meet the load. Suppose each generator's cost (C) is a function of its power output P (in terms of units), and costs per unit are given by: C2 = 1 + 0.6P2 + P22 (for Generator 2). -1-P -Pi2 (for Generator 1), If the total...
a) Formulate a cost function along with constraints, if any, for the following optimization problems. You don't need to solve any of these problems. i) Two electric generators are interconnected to provide total power to meet the load. Suppose each generator's cost (C) is a function of its power output P (in terms of units), and costs per unit are given by: C2 = 1 + 0.6P2 + P22 (for Generator 2). -1-P -Pi2 (for Generator 1), If the total...
please help me the best you can
Part 1: Optimization with inequality constraints 1. A consumer lives on an island. Her utility function is U = (x²y)1/3. She produces two goods, x and y. She faces a production constraint and an environmental constraint: Her production possibility frontier is: x² + y2 s 300. She faces an environmental constraint given by x + y = 200. a) Set up the Lagrangian function. b) List all of the Kuhn-Tucker conditions. c) Interpret...
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