Final answer:
The minimum value for the equation Q = 6x + 6y + 8, given the constraints, occurs at the coordinates (-4, 0). This conclusion is reached by evaluating the objective function at the vertices of the feasible region described by the constraints.
Step-by-step explanation:
The question centers on finding the coordinates where the minimum value occurs for the linear equation Q = 6x + 6y + 8, subject to several constraints. These constraints are x ≥ -4, -3x + 4y ≥ 0, and 2x + 4 ≤ 20. To find the minimum value, we must check the vertices of the feasible region defined by the constraints
The feasible region is the intersection of these constraints. Since Q is a linear function, its minimum value will occur at one of the vertices of the feasible region. By evaluating the objective function Q at the vertices given in the options, we can find the minimum value. Option (a) coordinates (-4, 0) satisfies all the constraints, and when substituting these values into Q, we get Q = 6(-4) + 6(0) + 8 = -16. No need to evaluate further options because the other vertices either do not satisfy the constraints or have a larger Q value.