# Assignment 6

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Last updated: May 17, 2019

HW 6A Multiple Choice Identify the choice that best completes the statement or answers the question. __D__1. An integrality condition indicates that some (or all) of the? a.

|RHS values for constraints must be integer| b. |objective function coefficients must be integer| c. |constraint coefficients must be integer| d. |decision variables must be integer| __A__2. Which of the following are potential pitfalls of using a non-zero suboptimality tolerance factor? a. |No assurance the returned solution is optimal. | b. |No assurance the returned solution is integer.

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| c. The true optimal solution may be worse than the returned solution. | d.

|There are no pitfalls to consider since the Solver will obtain solutions quicker. | __D__3. An ILP problem has 5 binary decision variables.How many possible integer solutions are there to this problem? a. |5| b. |10| c.

|25| d. |32| __C__4. Consider the constraint X3 + X4 + X5 + X6 + X7 ? 27 representing Air Express’ Monday worker requirement.

Why was a “? ” used versus an “=”? a. |The “? ” is needed to accommodate workers held over from Sunday. | b. |Solver only accepts “? ” constraints. | c. The “? ” is less restrictive. | d.

|The “=” will always produce an infeasible constraint. | __D__5. A production company wants to ensure that if Product 1 is produced, production of Product 1 not exceed production of Product 2. Which of the following constraints enforce this condition? a.

|X1 ? M2Y2| b. |X1 ? M2X2| c. |X1 ? M1Y1 , X1 ? Y1X2| d. |X1 ? X2| __D__6. A company will be able to obtain a quantity discount on component parts for its three products, X1, X2 and X3 if it produces beyond certain limits. To get the X1 discount it must produce more than 50 X1’s.

It must produce more than 60 X2’s for the X2 discount and 70 X3’s for the X3 discount. Which of the following pair of constraints enforces the quantity discount relationship on X3? a. |X31 ? M3Y3 , X32 ? 50Y3| b. |X31 ? M3Y3 , X31 ? 50| c.

|X32 ? (1/50)X31 , X31 ? 50| d. |X32 ? M3Y3 , X31 ? 50Y3| __D__7. The optimal relaxed solution for an ILP has X1 = 3. 6 and X2 = 2. 9. If we branch on X1, what constraints must be added to the two resulting LP problems? a.

|X1 ? 3, X1 ? 4| b. |X1 = 4| c. |3 ? X1, X1 ? 4| d. |X1 ? 3, X1 ? 4|

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