Question 1197130
x = number of ounces of product X.
y = number of ounces of product Y.


your constraint inequalities are:
9x + 4y >= 16 (ounces of protein constraint)
12x + 10y <= 50 (ounces of carb constraint)
x + y >= 2 (total ounces constraint)
x >= 0
y >= 0
9x + 4y = 16


the first 3 are the inequalities you are looking for.
the next 2 are for graphing purposes to make sure the ounces of either product are greater than or equal to 0.
the last one is to identify where exactly 16 grams of protein are situated on the graph.

your objective function is x + y because you want to find the minimum number of ounces of food that give you exactly 16 ounces of protein.


using the desmos.com calculator, you would graph the opposite of the inequalities and you would evaluate the objective function at the corner points of the feasible region.


the feasible region is the area on the graph that is not shaded.


you can see from the graph that your solution will lie on the line of the equation of 9x + 4y = 16
there are two possibilities.
(x,y) = (0,4) and (1.6,.4)
the objective function is x + y.
that's what you want to minimize.
at (0,4), x + y = 4
at (1.6,.4), x + y = 2


the minimum ounces of food that contain exactly 16 grams of protein are 1.6 ounces of product X and .4 ounces of product Y.


here's your graph.
<img src = "http://theo.x10hosting.com/2022/101201.jpg" >


let me know if you have any questions regarding this.
theo