A forest fire is burning down a narrow valley 3 miles wide at a speed of 40 feet per minute. The fire can be contained by cutting a fire break through the forest across the valley. It takes 30 seconds for one person to clear one foot of the firebreak. The value of lost timber is $4000 per square mile. Each person hired is paid $12 per hour, and it costs $30 to transport and supply each person with the appropriate equipment. Develop a model to determine:
a. how many people should be sent to contain the fire
b. the best location for the firebreak.