For the constraints given below,which point is in the feasible solution space of this minimization problem? (1)14x + 6y 42 (2)x + 3y 6
A)x = 0.5,y = 5.0
B)x = 0.0,y = 4.0
C)x = 2.0,y = 5.0
D)x = 1.0,y = 2.0
E)x = 2.0,y = 1.0

Question

For the constraints given below,which point is in the feasible solution space of this minimization problem? (1)14x + 6y > 42 (2)x + 3y > 6
A)x = 0.5,y = 5.0
B)x = 0.0,y = 4.0
C)x = 2.0,y = 5.0
D)x = 1.0,y = 2.0
E)x = 2.0,y = 1.0

Quizplus · Accepted Answer

For a point to be in the feasible solution space of the given minimization problem, it must satisfy all the given constraints. Let's check each option:A) Substituting x = 0.5 and y = 5.0 into the constraints:(1) 14(0.5) + 6(5.0) = 7 + 30 = 37, which does not satisfy 14x + 6y > 42.(2) 0.5 + 3(5.0) = 0.5 + 15 = 15.5, which satisfies x + 3y > 6.B) Substituting x = 0.0 and y = 4.0 into the constraints:(1) 14(0.0) + 6(4.0) = 0 + 24 = 24, which does not satisfy 14x + 6y > 42.(2) 0.0 + 3(4.0) = 0 + 12 = 12, which satisfies x + 3y > 6.C) Substituting x = 2.0 and y = 5.0 into the constraints:(1) 14(2.0) + 6(5.0) = 28 + 30 = 58, which satisfies 14x + 6y > 42.(2) 2.0 + 3(5.0) = 2 + 15 = 17, which satisfies x + 3y > 6.Thus, option C satisfies both constraints.D) Substituting x = 1.0 and y = 2.0 into the constraints:(1) 14(1.0) + 6(2.0) = 14 + 12 = 26, which does not satisfy 14x + 6y > 42.(2) 1.0 + 3(2.0) = 1 + 6 = 7, which satisfies x + 3y > 6.E) Substituting x = 2.0 and y = 1.0 into the constraints:(1) 14(2.0) + 6(1.0) = 28 + 6 = 34, which does not satisfy 14x + 6y > 42.(2) 2.0 + 3(1.0) = 2 + 3 = 5, which does not satisfy x + 3y > 6.Therefore, only option C is in the feasible solution space.

For the Constraints Given Below,which Point Is in the Feasible