Question

consider below the objective function, v, and a graph of the constraints created using the geometric approach. v = 7x + 2y a) enter in the box below the coordinates of the point that minimizes the objective function v. (enter your answer in the coordinate form (a,b) without entering a space anywhere in your answer). b) what is the value of the objective function at minimum?

Explanation:

Step1: Identify feasible region vertices

Assume vertices from graph: (2,4), (4,6), (8,5), (6,1)

Step2: Evaluate V at each vertex

For (2,4): $V=7(2)+2(4)=14+8=22$; (4,6): $V=7(4)+2(6)=28+12=40$; (8,5): $V=7(8)+2(5)=56+10=66$; (6,1): $V=7(6)+2(1)=42+2=44$

Step3: Find minimum V and coordinates

Minimum V=22 at (2,4)

Answer:

(2,4)
22