A soda producer makes and sells two products

A soda producer makes and sells two products, Classic Cola and Diet Cola. If this company spends X1 dollars on promotion of Classic Cola in a particular western city, it can sell at 75 X1^ 0.5 12-packs of Classic Cola each week there. Moreover, if this company spends X2 dollars on promotion of Diet Cola in a particular western city, it can sell at 50X2^0.5 12-packs of Diet Cola each week there. Each 12-pack of Classic Cola sells for $3.00 and costs $0.80 to produce and ship to customers in this western city. Each 12-pack of Diet Cola sells for $3.50 and costs $1.00 to produce and ship to customers in this western city. A total of $10,000 is available for promotion each week in this city. The soda producer seeks to maximize its weekly profit. Formulate and solve an appropriate optimization model to help this soda producer identify the best promotional strategies for its two products.

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