What are the three common elements of an optimization problem? objectives, resou
ID: 1720022 • Letter: W
Question
What are the three common elements of an optimization problem? objectives, resources, goals. decisions, constraints, an objective. decision variables, profit levels, costs. decisions, resource requirements, a profit function. In a linear programming problem, a valid objective function can be represented as Max Z = 5xy Max Z = 5x^2 + 2y^2 Max Z = 3x + 3y + z/3 Min Z = (x1 + x2)/x3 The following linear programming problem has been written to plan the production of two products. The company wants to maximize its profits. X_1 = number of product 1 to produce X_2 = number of product 2 to produce How main units of product 1 produced? An LP problem with a feasible region will have an optimal solution at some interior point. an optimal solution at some corner point. an optimal solution only at the origin. an optimal solution at two interior point. The following diagram shows the constrains for a LP model. Assume the point (0, 0) satisfies constraint (B, J) but does not satisfy constraints (D, H) or (C, J). Which set of points on this diagram defines the feasible solution space?Explanation / Answer
(1)
The three common elements of an optimization problem are objectives , resources and goals. What are the objectives of the problem are to be identified and what resources are available to solve the optimization problem are to be recognised and the goals to be achieved.
hence the answer is option (a)
(2)
In a linear programming problem valid objective function is represented as Max Z=5x2+2y2
hence the answer is option (b)
(3)
As there are two resources 2 units of resource 1 are to be consumed by each unit of product 2 produced.
hence the answer is option (b)
(4)
Feasible region is defined as the region between the set of ordered pairs that satisfy a system of given inequalities.
A linear programming problem with a feasible region will have an optimal solution at some interior point.
hence the answer is option (a)
(5)
From the figure it is clear that (0,0) satisfies the constraint (B,J) means it should lie between the line BJ and it doesnot satisfy constraints (D,H) or (C,I) that means the point should not fall in between the line DH and CI,so the feasible region is between I,F,G,J.
hence the answer is I,F,G,J
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