Question: a clothing store and a jewelry store are located side...
A clothing store and a jewelry store are located side by side in a small shopping mall. The number of customers who come to the shopping mall intending to shop at either store depends on the amount of money that the store spends on advertising per day. Each store also attracts some customers who came to shop at the neighboring store. If the clothing store spends $xC per day on advertising, and the jeweler spends $xJ on advertising per day, then the total profits per day of the clothing store are 𝜋𝐶(𝑥𝐶, 𝑥𝐽) = 60𝑥𝐶 + 𝑥𝐶𝑥𝐽 − 2𝑥𝐶 2 , and the total profits per day of the jeweler are 𝜋𝐽(𝑥𝐶, 𝑥𝐽) = 105𝑥𝐶 + 𝑥𝐶𝑥𝐽 − 2𝑥𝐽 2 . (In each case, these are profits net of all costs, including advertising.)
The extra profit that each store would get from an extra dollar’s worth of advertising by the other store is approximately equal to the derivative of that store’s profits with respect to the other store’s advertising expenditure. Estimate the jeweler’s extra profit from a dollar’s worth of advertising by the clothing store and the clothing store’s extra profit from an extra dollar’s worth of advertising by the jeweler.