Exam 3: Introduction to Optimization Modeling

Suppose the shadow price for a constraint is $12 and the allowable increase and decrease for the right hand side of the constraint are 25 (increase)and 10 (decrease).If the right hand side of that constraint were to increase by 10 the shadow price changes.

If a manufacturing process takes 4 hours per unit of x1and 2 hours per unit of x2 and a maximum of 100 hours of manufacturing process time are available,then an algebraic formulation of this constraint is:

Shadow prices are associated with nonbinding constraints,and show the change in the optimal objective function value when the right side of the constraint equation changes by one unit.

If a constraint has the equation 5x₁+ 2x₂ ≤ 60,then the constraint line passes through the points (0,12)and (30,0).

Consider the following linear programming problem:The above linear programming problem:Maximize4x₁ + 2x₂ Subject to: 4x₁ + 2x₂ ≤ 40 2x₁ + x₂≥ 20 x₁,x2 ≥ 0

When the profit increases with a unit increase in a resource,this change in profit will be shown in Solver's sensitivity report as the:

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

Linear programming models have three important properties.They are:

Exhibit 3-1 A winemaker in California's Napa Valley must decide how much of two types of wine she will produce from a particular variety of grapes. Each liter of table wine yields $8 profit, while each liter of dessert wine produces $3 profit. The labor hours and bottling process time used for type of wine are given in the table below. Resources available include 200 labor hours and 80 hours of bottling process time. Assume the winemaker has more than enough grapes available to supply any feasible production plan. Table Dessert Labor (Hours) 0.20 0.60 Process Time (Hours) 0.30 0.10 ​ -[Part 1] Refer to Exhibit 3-1.Formulate a linear programming model that will enable the winemaker to determine the number of liters of each type of wine to produce in order to maximize her profit.

Suppose a company sells two different products,x1and x2,for net profits of $6 per unit and $3 per unit,respectively.The slope of the line representing the objective function is: