Suppose that a hot dog vendor uses a cart (K) and his time (L) to make and sell hot dogs. The vendor's production function is, whereQis the number of hot dogs per day. Suppose that the rental on hot dog carts is $50 per day and that the vendor wants to produce 500 hot dogs per day. Use calculus to:

a. derive the demand for labor.

b. show that the demand for labor satisfies the law of demand.