Mathes Inequalities

1. A second hand car showroom has a space of 420 m^2 for displaying two different models of cars: a family car and a sport car. A family car needs 8 m^2 of space and a sports car needs 10 m^2 of space for display. The cost for displaying a family car and a sport car is $300 and $600 respectively. The total cost for the display should not exceed $18000. Asume that there are x family cars and y sports cars displayed.
The constraints are: 8x+10y(<=)420...(1)
300x+600y<=18000...(2)
x and y are non negative integers...(3)
The net profit on selling a family car and a sport car is $6000 and $10000 respectively. Asume that all the cars displayed will be sold. 40 family cars should be displayed to get the maximum profit $340000. (If the number of family cars sold is at least five times the number of sports cars sold, find the maximum profit and the corresponding number of family cars sold)