Problem $2(20$ points$).$ A company has a budget $of$ $$20,000$ for advertising its product and

two options: platforms A and $B.$ A potential customer gets exposed $to$ the product $if$ they see the

$ad$ for the first time. Each $adon$ platform A costs $$1,000$ and generates exposures $as$ follows: ads

$1-6,10,000$ exposures, ads $7-10,2,000$ exposures, ads $11-15,2,500$ exposures, and any $ad$ after

$16$ gets $0$ exposure. Each $adon$ platform $Bis$ costs $$1,200$ and generates exposures $as$ follows: ads

$1-4,8,000$ exposures, ads $5-12,6,000$ exposures, ads $13-15,2,000$ exposures, and any $ad$ after

$16$ gets $0$ exposure. Assume that the two platforms A and $B$ have $no$ overlaps $in$ the customers.

Write $an(mixed-)integer$ linear optimization model $to$ maximize the exposures $of$ the

product. Use computer tools $to$ find $an$ optimal solution $to$ this model.