Applications of the Derivative

4. A forest fire is burning in a valley. Officials estimate that if the fire burns for h hours, the cost of the lost timber is 1000h dollars. They estimate that x firefighters can stop the fire in 3600 hours. The cost for each firefighter is $20 (for transportation) plus $25 per hour (for salary, meals, and other overhead). A. Let C be the cost of the fire (including the cost of the firefighters and the lost timber). C will depend on both h (how many hours the fire burns) and x (the number of firefighters sent to fight it). Give a formula for C in terms of x and h. B. Give a formula that relates x and h. C. How many firefighters should be used if the cost C of the fire is to be minimized? Justify your solution