Part $1$: LP Modeling $(30$ marks$)$ A company is planning for its marketing campaign to promote three types of products: Product $1,$ Product $2,$ and Product $3.$ The marketing campaign consists of purchasing three types of advertisements: TV ads, Print ads, and Radio ads. A TV ad will cost $$30,000$ each and increases the sale of Product $1$ by $2\%,$ increases the sale of Product $2$ by $1\%,$ and has no impact on the sale of Product $3.$ A Print ad will cost $$20,000$ each and increases the sale of Product $1$ by $3\%,$ increases the sale of Product $2$ by $2\%,$ and decreases the sale of Product $3$ by $1\%.$ A Radio ad will cost $$15,000$ and has no impact on the sale of Product $1,$ decrease the sale of Product $2$ by $1\mathrm{.}5\%,$ and increases the sale of Product $3$ by $4\%.$ In the coming week, the company can buy any number of Print ads, but can only buy up to $55$ and $35$ TV ads and Radio ads, respectively. The company intends to boost the sale of Product $1,$ Product $2,$ and Product $3,$ by at least $12\%,15\%,$ and $9\%,$ respectively, in the coming week. In addition, the number of TV ads purchased should not exceed the number of Print ads and Radio ads by $10$ and $13,$ respectively. Formulate an LP model for the above business problem $($DO NOT SOLVE THE MODEL$)$