Consider a boutique hat store that is trying to decide where to locate a new cadet. There are too many possible locations. one in a high-income community, where montidy is 510.000, and coz a middle-income community, where monthly income B $5.000. In both communities, the store's potential customers are spread along a line at one-kilometre increments along the line there are clusters of 100 potential customers, in bath communities, a consumer will buy one hat per month, provided the total price that they par, including the cost of transportation, is not more than 0.00250), where is the consumer's monthly income. The price of a hat at the store in either community is $10 Round trip transportation costs are 0.000110 per kilometre.


Question

(a) Solve for the store's market area and total sales (in units) if it is located in a high-income community.

(b) Solve for the store's market area and total sales (in units) if it is located in the middle-income community. 

(c) Suppose that the cost per month of operating the store, excluding any payment for real estate space, is 10,000+2Q, where Q is total sales. Calculate the profit per month of the new outlet if it is located in the high-income community and its profit if it is located in the middle income community,