Limited resources are modeled in optimization problems as a. an objective function b. constraints c. decision...
Limited resources are modeled in optimization problems as
a. an objective function
b. constraints
c. decision variables
d. alternatives
Homework Answers
Answer
Option b
constraints
A limited resource is constraints.
limited availability of raw material is a constraint for the optimization.
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Limited resources are modeled in optimization problems as
a. an objective function
b. constraints
c. decision...
9. In optimization problems with inequality constraints, the value of the Lagrange function, in an optimum:...
9. In optimization problems with inequality constraints, the value of the Lagrange function, in an optimum: a) equals the value of the objective function. b) may be smaller than the value of the objective function. c) is always smaller than the value of the objective function. d) may be greater than the value of the objective function. e) is always greater than the value of the objective function.
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.
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...
When many constraints are present in a linear optimization problem, there is a greater chance that...
When many constraints are present in a linear optimization problem, there is a greater chance that a redundant constraint exists. Assume you are trying to maximize an objective function and you have two decision variables, X1 and X2. If a redundant constraint exists, does the constraint become necessary if you try to minimize (instead of maximize) the same objective function? Why? Do you need an objective function to determine if a constraint is redundant? Explain.
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...
Show decision variables, objective function and constraints. Use excel solver to solve the problem. The Ferguson...
Show decision variables, objective function and constraints. Use excel solver to solve the problem. The Ferguson Paper Company produces rolls of paper for use in adding machines, desk calculators, and cash registers. The rolls, which are 200 feet long, are produced in widths of 1.5, 2.5, and 3.5 inches. The production process provides 200-foot rolls in 10-inch widths only. The firm must therefore cut the rolls to the desired final product sizes. The current requirements (e.g. pre-orders) for the three...
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...
10. In optimization problems with inequality constraints, the Kuhn-Tucker conditions are: a) sufficient conditions for (x0,...
10. In optimization problems with inequality constraints, the Kuhn-Tucker conditions are: a) sufficient conditions for (x0, ..., xN ) to solve the optimization problem. b) necessary conditions for (x0, ..., xN ) to solve the optimization problem. c) sufficient but not necessary conditions for (x0, ..., xN ) to solve the optimization problem. d) neither sufficient nor necessary conditions for (x0, ..., xN ) to solve the optimization problem. e) none of the above.
(A) Identify and define your variables (b) Write the objective function (c) Write the constraints A...
(A) Identify and define your variables (b) Write the objective function (c) Write the constraints A calculator company produces a scientific calculator and a graphing calculator. Long-term projections indicate an expected demand of at least 110 scientific and 120 graphing calculators each day. Because of limitations on production capacity, no more than 160 scientific and 180 graphing calculators can be made daily. To satisfy a shipping contract, a total of at least 200 calculators much be shipped each day. If...
Find the solution of the objective function for problems (a) - (b) below. For each problem,...
Find the solution of the objective function for problems (a) -
(b) below. For each problem, confirm that the optimum satisfies the
Kuhn-Tucker conditions. At each solution, describe whether the
constraint(s) is binding.
Mathematics for Economists Ken Danger Problem Set 13 1) Find the solution of the objective function for problems (a) - (b) below. For each problem, confirm that the optimum satisfies the Kuhn-Tucker conditions. At each solution, describe whether the constraint(s) is binding. a) Minimize the cost function...
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...
Find the solution of the objective function for problems (a) -
(b) below. For each problem, confirm that the optimum satisfies the
Kuhn-Tucker conditions. At each solution, describe whether the
constraint(s) is binding.
Mathematics for Economists Ken Danger Problem Set 13 1) Find the solution of the objective function for problems (a) - (b) below. For each problem, confirm that the optimum satisfies the Kuhn-Tucker conditions. At each solution, describe whether the constraint(s) is binding. a) Minimize the cost function...
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