Two Stores Are Located Side by Side and Attract Customers

Two stores are located side by side and attract customers to each other and to themselves by advertising. Where x₁ and x₂ are the advertising expenditures of stores 1 and 2, the profits of the firms are (48 + x₂) x₁ - 2(x₁) ² for store 1 and (54 + x₁) x₂ - 2(x₂) ² for store 2. Knowing these functions, one investor buys both stores. In order to maximize his total profits, how much should he spend on advertising for store 1?

A) $10
B) $26
C) $25
D) $35
E) None of the above.

Correct Answer:

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