# Determine lot size with extra constraints and EOQ formula

Given a fixed price of 250,00 dollars for the warehouse and the price of the product is 5,00 dollars per product.

The order cost is 500,00 dollars but if more than 1000 products are ordered then it will increase to 625 dollars.

The warehouse has maximum capacity of 1500 pieces and for every extra piece (above 1500) 0,1 dollars are changed per day per product/piece.

Assume a month has 30 days and per day 100 pieces are sold.

Determine the optimal order size and cost price.

I have to use EOQ formula with lagerange multiplier but i have no idea how to start.

More specifically i have to use following formula:

$$G(q_i,\lambda) = min\sum(\frac{q_i.c_i}{2} + \frac{r_ic_{pi}}{q_i}) + \lambda(\sum_ib_iq_i-B)$$

I have no idea how to incorporate extra costs in this formula.

Any help would be great and if there are alternative ways to solve this problem then they will be accepted also.