A museum director must decide how many guards should be employed to control a newly opened wing of a museum. Budget cuts have forced the director to station guards at the doors between rooms guarding two rooms at once. A map of the wing and different rooms (AJ) is shown below: D Door(s) F E B C Entrance a) Formulate an integer optimization problem to minimize the total number of required guards (while each of the rooms is controlled by at least one guard). Describe and explain your optimization model briefly. b) Implement and solve your model using CVX, MATLAB, or Python. How many museum guards are needed? What is the solution of the LP relaxation of your model?