Answer: 410 at (5/3, 14/3).
- A 410 at (5/3, 14/3)
- B 560 at (0,8)
- C 550 at (11,0)
- D All three give the same minimum
Correct answer: A. 410 at (5/3, 14/3)
Explanation: Z(0,8) = 50(0)+70(8) = 560. Z(11,0) = 50(11)+70(0) = 550. Z(5/3,14/3) = 50(5/3)+70(14/3) = 250/3+980/3 = 1230/3 = 410. The minimum cost is 410 at (5/3, 14/3).
The feasible region (shaded) is bounded by the constraint lines; the fundamental theorem of LPP guarantees the optimal value of the objective function occurs at one of the corner points (O, A, B, C), so only these need to be checked, not the entire region.
Concept context
Optimizing a linear objective function subject to linear constraints using the graphical corner point method.