Consider the Following Integer Linear Programming Problem The Solution to the Linear Programming Formulation Is: X1 =

question 7

Short Answer

Consider the following integer linear programming problem:

$\begin{array} { l l } \text { Max } Z = & 3 x _ { 1 } + 2 x _ { 2 } \\\text { Subject to: } & 3 x _ { 1 } + 5 x _ { 2 } \leq 30 \\& 4 x _ { 1 } + 2 x _ { 2 } \leq 28 \\& x _ { 1 } \leq 8 \\& x _ { 1 } , x _ { 2 } \geq 0 \text { and integer }\end{array}$
The solution to the linear programming formulation is: x1 = 5.714, x2 = 2.571.
What is the optimal solution to the integer linear programming problem?
State the optimal values of decision variables and the value of the objective function.

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