The output at a certain factory is Q(K, L) = (K 1 3 +L 2 3 ) 2 units per day, where K is the capital needed in $1,000 needed and L is the labor used in 100 person-hours.

Currently, $5,000 of capital and 400 person-hours of labor are used. (a) Use calculus to approximate the actual change in output that will result next week if the plan for next week is to change the capital to $4,000 and the labor to 500 person-hours.