## Test Bank For Practical Management Science 5 Edition Wayne L Winston S Christian Albright

**Chapter 3 – Introduction to Optimization Modeling**

1.Â In an optimization model, there can only be one:a.Â decision variableb.Â constraintc.Â objective functiond.Â shadow price*ANSWER:Â Â *c*POINTS:Â Â *1Â Â 2.Â In using Excel to solve linear programming problems, the changing cells represent the:a.Â value of the objective functionb.Â constraintsc.Â decision variablesd.Â total cost of the model*ANSWER:Â Â *c*POINTS:Â Â *1Â Â 3.Â The condition of *nonnegativity* requires that:a.Â the objective function cannot be less that zerob.Â the decision variables cannot be less than zeroc.Â the right hand side of the constraints cannot be greater then zerod.Â the reduced cost cannot be less than zero*ANSWER:Â Â *b*POINTS:Â Â *1Â Â 4.Â If a manufacturing process takes 4 hours per unit of *x* and 2 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:a.Â 4*x* 2*y*â‰¥ 100b.Â 4*x*âˆ’ 2*y*â‰¤ 100c.Â 4*x* 2*y*â‰¤ 100d.Â 4*x*âˆ’ 2*y*â‰¥ 100*ANSWER:Â Â *c*POINTS:Â Â *1Â Â 5.Â The feasible region in all linear programming problems is bounded by:a.Â corner pointsb.Â hyperplanesc.Â an objective lined.Â all of these options*ANSWER:Â Â *b*POINTS:Â Â *1Â Â 6.Â Suppose a company sells two different products, *x* and *y*, for net profits of $6 per unit and $3 per unit, respectively. The slope of the line representing the objective function is:a.Â 0.5b.Â âˆ’0.5c.Â 2d.Â âˆ’2*ANSWER:Â Â *d*POINTS:Â Â *1Â Â 7.Â The equation of the line representing the constraint 4*x* 2*y*â‰¤ 100 passes through the points:a.Â (25,0) and (0,50)b.Â (0,25) and (50,0)c.Â (âˆ’25,0) and (0,âˆ’50)d.Â (0,âˆ’25) and (âˆ’50,0)*ANSWER:Â Â *a*POINTS:Â Â *1Â Â 8.Â 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:a.Â add-in priceb.Â sensitivity pricec.Â shadow priced.Â additional profit*ANSWER:Â Â *c*POINTS:Â Â *1Â Â 9.Â Linear programming models have three important properties. They are:a.Â optimality, additivity and sensitivityb.Â optimality, linearity and divisibilityc.Â divisibility, linearity and nonnegativityd.Â proportionality, additivity and divisibility*ANSWER:Â Â *d*POINTS:Â Â *1Â Â 10.Â Consider the following linear programming problem:Maximize 4*x*_{1} 2*y*_{2}Subject to:4*x*_{1} 2*y*_{2}â‰¤ 402*x*_{1} *y*_{2}â‰¥ 20*x*_{1}, *y*_{2}â‰¥ 0The above linear programming problem:a.Â has only one feasible solutionb.Â has more than one optimal solutionc.Â exhibits infeasibilityd.Â exhibits unboundedness*ANSWER:Â Â *c*POINTS:Â Â *1

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