The manager of a company estimates that it will cost $10,000 to produce 400 units of her product 1 year from now and that all those units can then be sold at a price of $30 per unit. She also estimates that in 1 year, the price will be increasing at the rate of 75 cents per unit per month, while the level of production will be decreasing at the rate of 2 units per month and the cost will stay constant.

If x is the level of production at time t, where t = 0 is 1 year from now, what is the profit P(x)? Find the rate at which the profit will be changing 1 year from now with respect to x. Will the profit be increasing or decreasing at that time?