A clothing store and a jeweler are located side by side in a shopping mall.If the clothing store spends C dollars on advertising and the jeweler spends J dollars on advertising, then the profits of the clothing store will be (18+ J)C - C² and the profits of the jeweler will be (36 + C)J - 2J ².The clothing store gets to choose its amount of advertising first, knowing that the jeweler will find out how much the clothing store advertised before deciding how much to spend.The amount spent by the clothing store will be A)54. B)9. C)36. D)18. E)27.

Question

Quizplus · Accepted Answer

To maximize the profit of the clothing store, we need to find the value of C that maximizes the expression (18F1F1F1S1 + F1F1F10J)C - (F1F1F10C2S1 + F1F1F10JC²). Let's simplify this expression by collecting like terms: (18F1F1F1S1 + F1F1F10J)C - (F1F1F10C2S1 + F1F1F10JC²) = (18F1F1F1S1 + F1F1F10J - F1F1F10J)C - F1F1F10C2S1 = (18F1F1F1S1)C - F1F1F10C2S1 To maximize this expression, we need to take the derivative with respect to C, set it equal to zero, and solve for C: d/dC[(18F1F1F1S1)C - F1F1F10C2S1] = 0 18F1F1F1S1 - 2F1F1F10CS1 = 0 C = (9F1F1F1S1)/(F1F1F10) Since C is positive, we can ignore the negative solution. Therefore, the clothing store should spend 18F1F1F1S1 + F1F1F10J = 18F1F1F1S1 + F1F1F10(2J) = 18F1F1F1S1 + 2F1F1F10J dollars on advertising to maximize its profit.

A Clothing Store and a Jeweler Are Located Side by Side