$Y_1=200x_1-0\mathrm{.}001x_1^2$

$Y2=400x_2-0\mathrm{.}002x_2^2$

$Y3=100x_3-0\mathrm{.}0001x_3^2$ Imagine you are a marketing manager for a new beverage company launching a refreshing energy drink. Your goal is to maximize brand awareness within a limited advertising budget. The marketing campaign includes three different social media channels. You have a budget of $$100,000$ Provide the total number of impressions with your plan by rounding to the next integer. for the entire campaign.

The number of impressions $($Yi$)$ that each social media channel provides as a function of the money allocated to that channel $($xi$)$ are given as follows:

Y$1=200$x$10\mathrm{.}001$x$12$

Y$2=400$x$20\mathrm{.}002$x$22$

Y$3=100$x$30\mathrm{.}0001$x$32$

For example, spending $$10,000$ on social media channel $1$ provides $1\mathrm{.}9$ million impressions.

Determine the optimal allocation of the budget to maximize the total number of impressions. Provide the total number of impressions with your plan by rounding to the next integer.