What are integer programming and mixed-integer programming problems? Provide examples to illustrate their usage.
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The following problem description represents Max 7X1 + 3X2 subject to 5X1 + 7X2 ≤ 27, 4X1 + X2 ≤ 14, 3X1 - 2X2 ≤ 9, X1, X2 ≥ 0, X1 integer. A. a binary programming problem B. a nonlinear programming problem C. a mixed-integer linear programming problem D. a pure integer programming problem E. a linear programming problem QUESTION 2 Solving an integer programming problem by rounding off answers obtained by solving it as a linear programming problem, we often find that A. all constraints are satisfied exactly. B. if the constraints are satisfied, the value of the objective function for a maximization problem will likely be less than that for the LP solution. C. the values of decision variables obtained by rounding off are always very close to the optimal values. D. the objective function value is zero. QUESTION 3 Which of the following is not a type of integer programming problem? A. zero-one programming problem B. mixed-integer programming problem C. blending problem D. pure integer programming problem QUESTION 4 The graphical solution method can be used to solve problems with more than two variables. True False
Md.Daniyal A.
Problem 11-1 (a) Indicate whether the following linear program is an all-integer linear program or a mixed-integer linear program. Max 30x1 + 25x2 s.t. 3x1 + 1.5x2 ≤ 400 1.5x1 + 2x2 ≤ 250 1x1 + 1x2 ≤ 150 x1, x2 ≥ 0 and x2 integer Write the LP Relaxation for the problem but do not attempt to solve. If required, round your answers to one decimal place. (b) Indicate whether the following linear program is an all-integer linear program or a mixed-integer linear program. Max 3x1 + 4x2 s.t. 2x1 + 4x2 ≥ 8 2x1 + 6x2 ≥ 12 x1, x2 ≥ 0 and integer Write the LP Relaxation for the problem but do not attempt to solve. If required, round your answers to one decimal place.
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