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 (42  J) C  C² and the profits of the jeweler will be (54  C) J  2J².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) 74.
B) 111.
C) 18.50.
D) 37.
E) 55.50.

Question

Kaylee Hassell · Accepted Answer

Final Answer : D, Explanation :  To maximize its profits, the clothing store wants to maximize the expression (42+10J)/(1-C), which represents its profit formula, before the jeweler chooses its advertising expenditure. Since J is a constant, (42+10J)/(1-C) is maximized when C is minimized. Therefore, the clothing store should choose C=0, which gives a profit of 42J for the clothing store. Once the clothing store has chosen C=0, the jeweler wants to maximize the expression (54C+J)/(1-2J), which represents its profit formula, knowing that C=0. Since C=0, the expression simplifies to J/(1-2J), which is maximized when J=1/4. Therefore, the jeweler should choose J=1/4, which gives a profit of 63/8 for the jeweler.

Definitions

Learning Objectives

Learning Objectives

Related questions