Aussie Maths & Science Teachers: Save your time with SmarterEd
For linear programming problems in general, which of the following statements is false?
A. The objective function is a linear expression.
B. The expressions defining the constraints are linear inequalities.
C. There may be more than one optimal solution.
D. The value of the objective function must be positive.
E. The constraints are used to define the feasible region.
`D`
`text(Consider)\ A`
`text(True, as objective function has to be)`
`text(linear for linear programming problems.)`
`:.\ text(Eliminate)\ A`
`text(Consider)\ B`
`text(True, as linear inequalities help define)`
`text(the region or constraints on the graph.)`
`:.\ text(Eliminate)\ B`
`text(Consider)\ C`
`text(True, as any point in the defined region)`
`text(can be an optimal solution.)`
`:.\ text(Eliminate)\ C`
`text(Consider)\ D`
`text(False, as depending on the point given)`
`text(that fits the constraints, the objective)`
`text(function may turn out to be negative)`
`text(when this point is substituted into the)`
`text(objective function.)`
`text(Similarly)\ E\ text(can be ruled out.)`
`=> D`