Exam 13: Introduction to Optimization Modeling

Suppose a liquor store sells beer for a net profit of $1 per unit and wine for a net profit of $2 per unit.Let x equal the amount of beer sold and y equal the amount of wine sold.An algebraic formulation of the profit function is:

It helps to ensure that Solver can find a solution to a linear programming problem if the model is well-scaled;that is,all of the numbers are of roughly the same magnitude.

The most important solution method for linear programming problems is known as the:

If a manufacturing process takes 3 hours per unit of x and 5 hours per unit of y and a maximum of 100 hours of manufacturing process time are available,then an algebraic formulation of this constraint is:

The equation of the line representing the constraint $2 x + 4 y \leq 80$ Passes through the points:

If a constraint has the equation $3 x + 2 y \leq 60$ ,then the constraint line passes through the points (0,20)and (30,0):

Proportionality,additivity,and divisibility are three important properties that LP models possess,which distinguish them from general mathematical programming models:.

The set of all values of the changing cells that satisfy all constraints,not including the nonnegativity constraints,is called the feasible region.

Nonbinding constraints will always have slack,which is the difference between the two sides of the inequality in the constraint equation.

In using Excel to solve linear programming problems,the target cell represents the:

Reduced costs indicate how much the objective coefficient of a decision variable that is currently 0 or at its upper bound must change before that the value of that variable changes.

In determining the optimal solution to a linear programming problem graphically,if the objective is to maximize the objective,we pull the objective function line down until it contacts the feasible region.

Infeasibility refers to the situation in which there are no feasible solutions to the LP model

All linear programming problems should have a unique solution,if they can be solved.

In linear programming we can use the shadow price to calculate increases or decreases in:

There are generally two steps in solving an optimization problem,model development and optimization.

Consider the following linear programming problem: Maximize $5 x _ { 1 } + 5 x _ { 2 }$ Subject to $x _ { 1 } + 2 x _ { 2 } \leq 8$ $x _ { 1 } + x _ { 2 } \leq 6$ $x _ { 1 } , x _ { 2 } \geq 0$ The above linear programming problem:

When using the graphical solution method to solve linear programming problems,the set of points that satisfy all constraints is called the:

Linear programming models have three important properties.They are:

Linear programming is a subset of a larger class of models called: