Determining a selling price for a new product is complex, as several parameters come into play. If you choose a price that is too high, you will not make many sales. On the other hand, if you choose a price that is too low, the business may not be profitable. A small business wants to maintain a certain inventory in each of its distribution points in order to achieve its profitability objective. It must set the selling price of a new product so that its weekly profit potential is $500. The quantity of products held in stock to sell is represented by the variable y and the quantity of products sold, by the variable x. The cost of maintaining the inventory (distribution cost) of each product is set at $10, but the selling price is not determined. The parameters that form the constraints are defined below.

x+y less than or equal to 18

y bigger than or equal to 8

y bigger than or equal to x

2x bigger than or equal to y+6

Determine the price at which the product must be sold to reach the $500 profit target while satisfying all the constraints and keeping the distribution cost at $10.