Question 1071240
x = number of units of product A.
y = number of units of product B.


your constraint inequalitiess are:


x >= 0
y >= 0
6x + 3y <= 2700
.2x + .3y <= 120


selling price is equal to 7x + 4y


profit is equal to 7x - 6x - .2x + 4y - 3y - .3y


combine like terms and you get:


profit is equal to .8x + .7y


that's your objective function.


using the desmos.com calculator, you would graph the opposite inequalities.


to be more specific, you would graph the following inequalities.


x <= 0
y <= 0
6x + 3y >= 2700
.2x + .3y >= 120


the area of the graph that is NOT shaded is your region of feasibility.


your graph will look like this.


<img src = "http://theo.x10hosting.com/2017/030301.jpg" alt="$$$" </>


you then find the corner points of this region and evaluate your objective function at those corner points.


you will get.


profit at (0,400) = 280
profit at (375,150) = 405
profit at (450,0) = 360


your maximum profit is at (375,150).


you have to meet your constraints at those corner points.


production costs at (375,150) = 6x + 4y = 2700 which meets the constraint that they be less than or equal to 2700.


transport costs at (375,150) = .2x + .3y = 120 which meets the constraint that they be less than or equal to 120.


x >= 0 and y >= 0 are also meet the constraint that they be greater than or equal to 0 at the point (375,150).


all constraints are met.


your maximum profit is when you sell 375 units of product A and 150 units of product B.