Question 1182966
x = number of barrels of type 1
y = number of barrels of type 2


your constraints are:


x + y <= 4000
2x + 3y <= 9000


your would graph the opposite of these inequalities in the desmos.com calculator.


the unshaded area is your region of feasibility.
the maximum profit is at the corners of the region of feasibility.


your graph looks like this:


<img src = "http://theo.x10hosting.com/2021/071301.jpg" >


your corner points are (x,y) = (0,3000), (3000,1000), (4000,0)


your objective function is 25x + 30y.
this is what you want to maximize.


you evalute the objective function at each of your corner points.


(0,3000) = 0 * 25 + 3000 * 30 = 90,000
(3000,1000) = 3000 * 25 + 1000 * 30 = 105,000
(4000,0) = 4000 * 25 + 0 * 30 = 100,000


your maximum profit is when you refine 3000 barrels of type 1 and 1000 barrels of type 2.


all your constraints need to be satisfied.


at your maximum point of (3000,1000), .....


x + y = 4000 <= 4000
2x + 3y = 2 * 3000 + 3 * 1000 = 6000 + 3000 = 9000 <= 9000


all your constraints are satisfied at your maximum profit point.


all looks good.


your solution is that 3000 barrels of type 1 and 1000 barrels of type 2 need to be refined for maximum profit.