Architectural Designs

LINEAR PROGRAMMING HELP??? PLEASE!!?

CAN ANYONE GIVE ME THE CONSTRAINTS FOR THIS PROBLEM? A builder has 60 lots on which he can build houses with one house on each lot. He builds two types of houses, colonial and ranch. Sales experience has taught him that he should plan to build at least 3 times as many ranch-style houses as colonial. If he makes a profit of $5000 on each colonial and $4500 on each ranch, how many of each kind should he build to maximize his profit? PLEASE HELP ME!!! THANKS!

Public Comments

1. y = num of colonials x = num of ranches you want to maximize profit (5000y + 4500x) subject to : 1. y + x <= 60; y <= -x +60 2. y <= 3x (3 times as many ranches or more than colonials) 4. y >= 0 Therefore the feasible regions is bounded by y <= -x + 60 and y <= 3x and y >= 0. Which would be the triangular regions formed by the following points (15, 45) , (60, 0), (0, 0) The max is one of those three points, either x = 15 and y = 45 or x = 60 and y = 0 or x = 0 and y = 0. plugging back in you find that x (num of colonials) = 15 y (num of ranches) = 45