$1)$Write down and explain the entire optimization problem describing the variables you choose, then write the objective in terms of the variables, and then write the constraints in terms of the variables.

$2)$Use solver to determine the total number of impressions per country in each category while revising the plan offered by the agency. Include your answer. Do you end up spending the entire budget of $$95000?$ Explain why or why not. $($Use dataset provided and background info$)$

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B$12$

$3000000$

A C D E F G H EXHIBIT $4$: Preliminary media Plan Proposed by Impact Marketing Ltd$.$ Market Indonesia Korea Malaysia Pakistan Philippines Singapore Tot$/$Avg Marketplace Ads Impressions $6,000,0006,000,0006,000,0001,000,0006,000,0002,000,00027,000,000$ CPM $ $0\mathrm{.}53$ $ $0\mathrm{.}88$ $ $0\mathrm{.}60$ $ $0\mathrm{.}57$ $ $0\mathrm{.}56$ $ $0\mathrm{.}71$ $ $0\mathrm{.}64$ Cost $ $3,180$ $ $5,280$ $ $3,600$ $ $570$ $ $3,360$ $ $1,420$ $ $17,410$ Premium Ads Impressions $3,500,0003,700,0003,700,000700,0003,700,0001,350,00016,650,000$ CPM $ $4\mathrm{.}41$ $ $5\mathrm{.}25$ $ $3\mathrm{.}22$ $ $4\mathrm{.}41$ $ $3\mathrm{.}85$ $ $5\mathrm{.}60$ $ $4\mathrm{.}30$ Cost $ $15,435$ $ $19,425$ $ $11,914$ $ $3,087$ $ $14,245$ $ $7,560$ $ $71,666$ Mobile Ads Impressions $3,000,0003,000,0003,000,0003,000,0003,000,00015,000,000$ CPM $ $0\mathrm{.}40$ $ $0\mathrm{.}40$ $ $0\mathrm{.}40$ $ $0\mathrm{.}40$ $ $0\mathrm{.}40$ $ $0\mathrm{.}40$ Cost $ $1,200$ $ $-$ $ $1,200$ $ $1,200$ $ $1,200$ $ $1,200$ $ $6,000$ Total Ads Impressions $12,500,0009,700,00012,700,0004,700,00012,700,0006,350,00058,650,000$ Cost $ $19,815$ $ $24,705$ $ $16,714$ $ $4,857$ $ $ $10,180$ $ $95,076$ Average CPM $ $1\mathrm{.}59$ $ $ $1\mathrm{.}32$ $ $1\mathrm{.}03$ $ $1\mathrm{.}48$ $ $1\mathrm{.}60$ $ $1\mathrm{.}62$ $ $95,076$

Background

The agency for Intel AP has provided to plan for getting ad$-$impressions across $3-$ad types $($FB

marketplace ads, FB premium ads and FB mobile ads$)$ across six countries in the Asia$-$Pacific region. The

plan details for this plan are seen in the "Original Plan" tab of the excel file $-$ "Intel AP Media Data $-$

Exercise".

The Intel AP team thinks that there is a need to update and optimize the agency's original plan. The first

reason is that the agency's plan shows only the ad$-$spend of $$95076$ but does not include the agency's

fee, which is $9\%$ of the ad$-$spend. Intel's total budget including the agency's fee is $$95000.$ The second

reason is that the plan included some assumptions about the typical CTRs for the different types of ads

and did not account for the social impression multiplier or the social CTR$.$ The social impression

multiplier accounts for the additional social impressions generated through clicks on premium and mobile ads. The social CTR is an estimate of the clicks generated from the ads generated by social impressions. Intel's team believed that based on previous data, they have better estimates of these parameters in different countries.

While updating the plan, Intel's team wants to ensure that this update should not result in more than $\backslash (125\backslash \%\backslash )$ of impressions in any country compared to the original plan. Further, the impressions should not fall below $\backslash (75\backslash \%\backslash )$ of the impressions generated through each category of ad in each country. This introduces a set of constraints that must be included in the solver formulation. In addition, there is another constraint that no mobile ads impressions are to be generated in Korea.