A biomedical intrumentation company sells its main product at the rate of 5 units per day. The instrument is manufactured in lots run every few days. It costs the company $2000 to setup for production of a lot and $40 per unit per day to hold finished instruments in inventory between runs.

The company would like to choose a lot size that minimizes average inventory and setup cost per day assuming that demand occurs smoothly at the given rate.

(a) Formulate a 1-variable unconstrained NLP to choose an optimum lot size.

(b) Plot the objective function of your model and compute an optimum lot size graphically.