Bonnie the buy-side trader is trying to figure out how to minimize trading costs for a large buy order. Bonnie has been instructed by the portfolio manager to buy 750,000 shares of Chocolate Chip, ticker CHCH. She subscribes to ITG TCA, and when she plugs in the order characteristics into the software, it spits out the following expected liquidity impact function (LI): LI = $3.00 *(1/N), where N is the number of (equal-sized) child orders used by the buy-side trader to fill the order. The x-axis in the figure below displays the number of child orders (N), and the y-axis displays the liquidity impact.

However, Bonnie the buy-side trader also knows that the price may move against her (increase) if she splits the order into too many executions. The ITG TCA software estimates the following expected fundamental price move (FPM): FPM=$0.004*(N-1)2 where N is again the number of (equal-sized) child orders used by the buy-side trader to fill the parent order. The x-axis in the figure below displays the number of child orders (N), and the y-axis displays the liquidity impact.

How many child-orders should she split her 750,000 shares of Chocolate Chip, ticker CHCH, into in order to minimize total expected trading costs? (Rounded to the nearest whole number) Hint: You do not need to solve the equations for N, just plug in discrete values in Excel.