Question 1202521
x = number of cases of baby wiggles.
y = number of cases of sleepy baby.


objective function is profit = 120x + 100y


constraint functions are:
5x + 3y <= 150 for raw material.
1x + 2y <= 44 for units of time.
x >= 0
y >= 0


using the desmos.com calculator at <a href = "https://www.desmos.com/calculator" target = "_blank">https://www.desmos.com/calculator</a>, you would graph the opposite of the constraint inequalities.
the area of the graph not shaded is your region of feasibility.
the corner points of this region would contain the maximum profit solution.
you would evaluate the objective function at each of these corner points to obtain the maximum profit.


the graph looks like this.


<img src = "http://theo.x10hosting.com/2023/052921.jpg">


profit = 120x + 100y
at (0,22), profit is equal to 2200
at (24,10), profit is equal to 3880
at (30,0), profit is equal to 3600


maximum profit is at (24,10).


all constraints need to be satisfied at that point.


constraint functions are:
5x + 3y <= 150 for raw material becomes 5*24 + 3 * 3 * 10 = 150.
1x + 2y <= 44 for units of time becomes 24 + 2*10 = 44.
x >= 0 and y >= 0.
all constraints are satisfied.


your solution is 24 cases of baby wiggles and 10 cases of sleepy baby will maximize profit.