# Optimization and Linear Programming

**Topics:**Optimization, Operations research, Linear programming

**Pages:**8 (1510 words)

**Published:**June 20, 2012

A common form of the product-mix linear programming seeks to find the quantities of items in the product mix that maximizes profit in the presence of limited resources. -True

Linear programming helps operations managers make decisions necessary to allocate resources. -True

In linear programming, the unit profit or unit contribution associated with one decision variable can be affected by the quantity made of that variable or of any other variable in the problem. -False

What combination of x and y will yield the optimum for this problem? Minimize $3x + $15y, subject to

(1) 2x + 4y 12 and

(2) 5x + 2y 10.

-x = 0, y = 0

In linear programming, a statement such as "maximize contribution" becomes a(n) -objective function.

Choosing the best alternative in the face of random states of nature is referred to as -decision thoery

Linear programming is part of larger body of knowledge referred to as optimization -True

One requirement of a linear programming problem is that the objective function must be expressed as a linear equation. -True

Which of the following is not one of the steps in setting up a LP formulation> -calculate the objective function

Which of the following represents valid constraints in linear programming? -2X + 7Y 100

finding the best decision to optimize a linear objective subject to multiple linear constarints is referred to as -Linear Programming

In linear programming, a statement such as "maximize contribution" becomes an objective function when the problem is formulated. -True

Linear programming helps operations managers make decisions necessary to allocate resources. -True

Linear programming is part of larger body of knowledge referred to as optimization -True

In linear programming, if there are three constraints, each representing a resource that can be used up, the optimal solution must use up all of each of the three resources. -False

DQ 20

In sensitivity analysis, a zero shadow price for a resource ordinarily means that the resource has not been used up. -True

What combination of a and b will yield the optimum for this problem? Maximize $6a + $15b, subject to

(1) 4a + 2b 12 and

(2) 5a + 2b 20.

-a = 0, b = 6

slack is associated with constraints

-True

Slack is associated with variables

-False

In linear programming, the unit profit or unit contribution associated with one decision variable can be affected by the quantity made of that variable or of any other variable in the problem. -False

In sensitivity analysis, a zero shadow price for a resource ordinarily means that

-the resource has not been used up

In terms of linear programming, the fact that the solution is infeasible implies that the "profit" can increase without limit.

-False

A shadow price reflects which of the following in a maximization problem? -the increase in profit that would accompany one added unit of a scarce resource

The slack for a <= constraint can be interpreted as

- The amount of a resource left over

A binding constraint is one that has

-Wrong amount of resource used greater than amount of resource available

choosing the best alternative in the face of random states of nature is referred to as -Wrong simulation, linear programming, linear regression

For the two constraints given below, which point is in the feasible solution space of this maximization problem? (1) 14x + 6y 42

(2) x - y 3

-Wrong x = 2, y = 1

An "=" type of constraint can have slack

-False

The optimal solution of a linear programming problem that consists of two variables and six constraints will probably not have all six constraints binding. -False

What combination of x and y will yield the optimum for this problem? Maximize $3x + $15y, subject to

(1) 2x + 4y 12 and

(2) 5x + 2y 10.

-x = 0, y = 3

If the Solver Results box indicates "Solver found a solution. All constraints and optimality conditions are satisfied" you can safely...

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