A biomedical intrumentation company sells its main product at the rate of 5 unit

Question

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.

Explanation / Answer

sol)

Let the amount of lot be 'x'

Now,

x/t = 5

where t is number of days for which the stock will be held

Cost per day,C = (2000 + 40*x*t)/t

using t = x/5

C = (2000 + 8x^2)/(x/5) = 10000/x + 40x

dC/dx = 0

-10000/x^2 + 40 = 0

x = 15.811 or 16

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