Exam 13: Introduction to Optimization Modeling

The solution of a linear programming problem using Microsoft Excel typically involves the following three stages:

If an LP model does have an unbounded solution,then we must have made a mistake - either we made an input error or we omitted one or more constraints.

Related to sensitivity analysis in linear programming,when the profit increases with a unit increase in a resource,this change in profit is referred to as the:

A linear programming problem with _____decision variable(s)can be solved by a graphical solution method.

All optimization problems include decision variables,an objective function,and constraints.

In some cases,a linear programming problem can be formulated such that the objective can become infinitely large (for a maximization problem)or infinitely small (for a minimization problem).This type of problem is said to be:

When the proportionality property of LP models is violated,then we generally must use non-linear optimization.

When formulating a linear programming spreadsheet model,there is one target (objective)cell that contains the value of the objective function.

The optimal solution to any linear programming model is a corner point of a polygon.

The proportionality property of LP models means that if the level of any activity is multiplied by a constant factor,then the contribution of this activity to the objective function,or to any of the constraints in which the activity is involved,is multiplied by the same factor.

What are the decision variables in this problem? Western Chassis produces high-quality polished steel and aluminum sheeting and two lines of industrial chassis for the rack mounting of Internet routers,modems,and other telecommunications equipment.The contribution margin (contribution toward profit)for steel sheeting is $0.40 per pound and for aluminum sheeting is $0.60 per pound.Western earns $12 contribution on the sale of a Standard chassis rack and $15 contribution on a Deluxe chassis rack.During the next production cycle,Western can buy and use up to 25,800 pounds of raw unfinished steel either in sheeting or in chassis.Similarly,20,400 pounds of aluminum are available.One standard chassis rack requires 16 pounds of steel and 8 pounds of aluminum.A Deluxe chassis rack requires 12 pounds of each metal.The output of metal sheeting is restricted only by the capacity of the polisher.For the next production cycle,the polisher can handle any mix of the two metals up to 4,000 pounds of metal sheeting.Chassis manufacture can be restricted by either metal stamping or assembly operations;no polishing is required.During the cycle no more than 2,500 total chassis can be stamped,and there will be 920 hours of assembly time available.The assembly time required is 24 minutes for the Standard chassis rack and 36 minutes for the Deluxe chassis rack.Finally,market conditions limit the number of Standard chassis racks sold to no more than 1,200 Standard and no more than 1,000 Deluxe.Any quantities of metal sheeting can be sold.

Suppose the allowable increase and decrease for an objective coefficient of a decision variable that has a current value of $50 are $25 (increase)and $10 (decrease).If the coefficient were to change from $50 to $60,the optimal value of the objective function would not change.

Consider the following linear programming problem: Maximize $2 x _ { 1 } + 2 x _ { 2 }$ Subject to $4 x _ { 1 } + 3 x _ { 2 } \geq 12$ $- 2 x _ { 1 } - 3 x _ { 2 } \leq 6$ $x _ { 2 } \geq 2$ $x _ { 1 } , x _ { 2 } \geq 0$ The above linear programming problem:

All optimization problems have:

It is instructive to look at a graphical solution procedure for LP models with three or more decision variables.

The additivity property of linear programming implies that the contribution of any decision variable to the objective is of/on the levels of the other decision variables.

Consider the following linear programming problem: Maximize $2 x _ { 1 } + 4 x _ { 2 }$ Subject to $x _ { 1 } + x _ { 2 } \leq 5$ $- x _ { 1 } + x _ { 2 } \geq 8$ $x _ { 1 } , x _ { 2 } \geq 0$ The above linear programming problem:

There are two primary ways to formulate a linear programming problem,the traditional algebraic way and in spreadsheets.

Suppose a company sells two different products,x and y,for net profits of $5 per unit and $10 per unit,respectively.The slope of the line representing the objective function is:

The feasible region in a graphical solution of a linear programming problem will appear as some type of polygon,with lines forming all sides.