Maximize Z = 5x + 4y subject to 2x + y ≤ 8, x + 2y ≤ 8, and x, y ≥ 0. What is the optimal value of Z?
Correct answer: C. 24
- A. 20
- B. 22
- C. 24
- D. 26
Explanation
The two constraint boundaries intersect at x = y = 8/3. This gives Z = 5(8/3) + 4(8/3) = 24, which exceeds the axis-corner values of 20 and 16.
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Linear programming models the maximum or minimum of an objective function subject to linear constraints. Questions involve translating word conditions into inequalities, drawing the feasible region, identifying corner points and evaluating the objective function, including cases involving non-negativity restrictions and redundant constraints.
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