$1.$ Integer Programming $[10$ points$]$

Sl y$-$Eye Beds wants to advertise its "Sleep System" to potential buyers.

A television commercial that costs $\backslash (\backslash$$ $25,000\backslash )$ will supposedly reach $50,000$ potential buyers. The breakdown of the audience is as follows:

A newspaper ad that costs $\backslash (\backslash$$ $7,000\backslash )$ will supposedly reach $30,000$ potential buyers. The breakdown of the audience is as follows:

A radio commercial that costs $\backslash (\backslash$$ $10,000\backslash )$ will supposedly reach $40,000$ potential buyers. The breakdown of the audience is as follows:

An online ad that costs $\backslash (\backslash$$ $15,000\backslash )$ will supposedly reach $60,000$ potential buyers. The breakdown of the audience is as follows:

The company has established several marketing guidelines. It wants to reach at least $375,000$ potential customers. It believes younger people are more likely to purchase this kind of bed than older people, so it wants to reach at least $1\mathrm{.}6$ times as many people under $40$ than $40$ and above. The company also believes that women are more likely to start the purchase process than men, so it wants its advertising audience to be at least $\backslash (60\backslash \%\backslash )$ female. Formulate and solve an integer programming model for this problem that will assist the company in determining the number of ads of each type it should use to minimize total cost.