Question 1198757
x = number of jumbo biscuits
y = number of regular biscuits


your constraint inequalities are:
x + y <= 400
2x + y <= 600


your objective function is:


income = .07x + .12y


x + y <= 400 says that the total number of biscuits has to be less than or equal to 400.


2x + y <= 600 says that the total amount of flour has to be less than 600 ounces.
there are 2 ounces of flour for each jumbo biscuit and 1 ounce of flour for each regular biscuit.


income = .07x + .12y says that income = 7 cents for each jumbo biscuit and 12 cents for each regular biscuit.


using the desmos.com/calculator, you would graph the opposite of the inequalities.
the area of the graph that is not shaded is your region of feasibility.
the region of feasibility includes the lines of the inequalities that border it.
the corner points of the region of feasibility is where the maximum income will be.


here is what the graph looks like:


<img src = "http://theo.x10hosting.com/2022/113005.jpg">


the corner points of the region of feasibility are:
(0,400)
(200,200)
(300,0)


you evaluate the objective function at each corner point to find the maximum income.


at (0,400), the income is 0 * .07 + 400 * .12 = 48
at (200,200), the income is 200 * .07 + 200 * .12 = 38
at (300,0), the income is 300 * .07 = 21


the maximum income is at the point (0,400)
that would require no large biscuits and 400 regular biscuits.