Exercise $13-39$ Algo

An online apparel retailer runs regular marketing campaigns on social media channels such as Facebook and Instagram. The retailer is considering four social media marketing campaigns on Facebook, Instagram, Pinterest, and Twitter for the four weeks prior to the December holiday season. However, due to its limited marketing budget, the retailer cannot run all four proposed campaigns. The following table describes the weekly cost $($in $$1,000)$ and the expected numbers of consumers each campaign will reach $($in $1,000).$

Marketing Cost Facebook Instagram Pinterest Twitter Weekly Budget

Week $14\mathrm{.}53\mathrm{.}53415$

Week $2544312$

Week $3435310$

Week $44\mathrm{.}545\mathrm{.}5212$

Consumers Reached $37303225$

a$.$ Formulate and solve the IP model to determine which of the four marketing campaigns the retailer should run in order to maximize the number of consumers reached, without going over its budget. What is the maximum number of consumers that the retailer can reach?

b$.$ Which social media channels should the retailer use in order to maximize the number of consumers reached?

c$.$ Will the retailer use up all of its marketing budget each week?