Problem $2(3$ pts$)$: You are the head of marketing for Galactic$-$LP Corp, a leading tech

company in the Andromeda Galaxy. Your team has just developed a new communication

device that translates alien languages in real$-$time. To promote this groundbreaking device,

you've identified three primary marketing channels within the galaxy: HoloNet Ads $($akin

to Social Media$),$ Quantum Search Ads, and Intergalactic Influencer Partnerships.

Each channel has its cost, reach, and efficiency. The challenge is to decide how much to

invest in each channel to maximize the number of Andromdians reached while staying within

your budget and ensuring you don't overuse specific channels.

Cost per unit of investment:

HoloNet Ads: $500$ Credits

Quantum Search Ads: $800$ Credits

Intergalactic Influencer Partnerships: $2,000$ Credits

Potential Andromdians reached per unit of investment:

HoloNet Ads: $10,000$ Andromdians

Quantum Search Ads: $7,000$ Andromdians

Intergalactic Influencer Partnerships: $40,000$ Andromdians

Marketing Budget: $100,000$ Credits

Channel Restrictions:

Maximum HoloNet Ads: $50$

Maximum Intergalactic Influencer Partnerships: $20$

Please do the following:

Formulate the LP in algebraic form.

Solve the LP and provide the solution.

Interpret the shadow prices and reduced costs for this problem.