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The LP relaxation of an integer programming (IP)problem is the same model as the IP model except that some integer constraints are omitted.

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True False

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False

If all the supplies and demands for a transportation model are integers,then the optimal Solver solution may or may not have integer-valued shipments.

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True False

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False

The optimal solution to an LP problem was 3.69 and 1.21.If and were restricted to be integers,then 4 and 1 will be a feasible solution,but not necessarily an optimal solution to the IP problem.

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True False

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False

The transportation model is a special case of the minimum cost network flow model (MCNFM).

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In blending problems,if a quality constraint involves a quotient,then the problem will be nonlinear.

True False

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If an LP problem is not correctly formulated,Solver will automatically indicate that it is infeasible when trying to solve it.

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Solver may be unable to solve some integer programming problems,even when they have an optimal solution.

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In network models of transportation problems,arcs represent the routes for getting a product from one node to another.

True False

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In a transportation problem,if it costs $4 per item to ship up to 200 items between cities,and $2 per item for each additional item,the proportionality assumption of LP is satisfied.

True False

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Integer programming (IP)models are optimization models in which all of the variables must be integers.

True False

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Transportation costs for a given route are nearly always linear and smooth,with the main cost differences occurring between routes.

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Many of the most successful applications of optimization in the real world have been in the areas of scheduling,blending,logistics,and aggregate planning.

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Logistics problems are problems of finding the least expensive way to transport products from their origin to their destination.

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In transportation problems,the three sets of input numbers that are required are capacities,demands,and flows.

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In transportation problems,shipments between supply points or between demand points are possible.

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Transshipment points are locations where goods neither originate nor end up,but goods are allowed to enter such points to be shipped out to their eventual destinations.

True False

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In transportation problem,shipping costs are often nonlinear due to quantity discounts.

True False

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If Solver fails to find an optimal solution to an integer programming problem,we might be able to find a near optimal solution by increasing the Integer Optimality setting.

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When we solve a linear programming problem with Solver,we cannot guarantee that the solution obtained is an optimal solution.

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