Suppose That a Hot Dog Vendor Uses a Cart (K)

Essay

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
, where Q is 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.