# Quantitative Methods - Integer programming

1. In using rounding of a linear programming model to obtain an integer solution, the solution is:
a. always feasible.
b. always optimal.
c. sometimes optimal and feasible.
d. always optimal and feasible.
e. never optimal and feasible.

2. The linear programming relaxation contains the objective function and the original constraints of the integer-programming problem but drops all ________.
a. decision variables
b. different variables
c. slack values
d. integer restrictions
e. nonnegativity constraints

3. If we are solving a 0-1 integer programming problem, the constraint x1 <= x2 is a ________ constraint.
a. Corequisite
b. mutually exclusive
c. conditional
d. multiple-choice
e. none of the above

4. Assume that we are using 0-1 integer programming model to solve a capital budgeting problem and xj = 1 if project j is selected and xj = 0 otherwise.
The constraint (x1 + x2 + x3 + x4 <= 2) means that ________ out of the 4 projects must be selected.
a. exactly 2, 4
b. at least 2, 4
c. exactly 1, 4
d. at most 2, 4

5. The branch and bound method of solving linear integer programming problems is ________.
a. a graphical solution
b. an enumeration method
c. an integer method
d. a relaxation method

6. The Wiethoff Company has a contract to produce 10000 garden hoses for a customer. Wiethoff has 4 different machines that can produce this kind of hose. Because these machines are from different manufacturers and use differing technologies, their specifications are not the same.

Fixed cost to set
Machine up production run Variable cost per hose Capacity
1 750 1.25 6000
2 500 1.50 7500
3 1000 1.00 4000
4 300 2.00 5000
The company wants to minimize total cost. Give the objective function.

a. Min 750y1+500y2+1000y3+300y4
b. 1.25x1+1.5x2+x3+2x4
c. Min 750y1+500y2+1000y3+300y4+1.25x1+1.5x2+x3+2x4
d. none of the above

7. If a maximization linear programming problem consists of all less than or equal to constraints with all positive coefficients and the objective function consists of all positive objective function coefficients, then rounding down the linear programming optimal solution values of the decision variables will ________ result in a feasible solution to the integer linear programming problem.

a. Sometimes
b. Never
c. Always

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Sarang Jagdale, PhD (IP)

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