let y = the number of pineapple pies.
the cost is equal to 15x + 30y.
the cost cannot exceed 300.
the inequality for that is 15x + 30y <= 300.
there must be at least 5 items.
the inequality for that is x + y >= 5.
your constraint inequalities are:
x + y >= 5
15x + 30y <= 300
using the desmos.com calculator, you would graph the opposite of these inequalities.
the area on the graph that is not shaded is your region of feasibility.
any coordinate point in the feasible region satisfies the requirements of the problem.
two other inequalities that need to be satisfied are x >= 0 and y >= 0 since the number of each can't be negative.
your constraint inequalities are:
x + y >= 5
15x + 30y <= 300
x >= 0
y >= 0
you graph the opposite of these inequalities.
here's what the graph looks like.
i chose 3 points in the feasible region.
they are:
(3,7)
(5,4)
10,2)
each of those points will satisfy every one of the constraint inequalities because they are in the region of feasibility.
algebraically, the constraints they must satisfy are:
the minimum value of x and y is 0.
the maximum value of x and y is defined by 15x + 30y <= 300.
when x = 0, 15x + 30y <= 300 becomes 30y <= 300 which results in y <= 10.
when y = 0, 15x + 30y <= 300 becomes 15x <= 300 which results in x <= 20.
your requirements are that x and y must each be greater than or equal to 0 and x must be less than or equal to 20 and y must be less than or equal to 10.
all these points satisfy those requirements.
the point (3,7) has 0 <= x <= 20 and 0 <= y <= 10.
the point (5,4) has 0 <= x <= 20 and 0 <= y <= 10.
the point (10,2) has 0 <= x <= 20 and 0 <= y <= 10.
on the graph, they are all in the feasible region, which is the unshaded area of the graph.
the graphing calculator used can be found at https://www.desmos.com/calculator
as an example:
when the point is (3,7), .....
x + y >= 5 becomes 3 + 7 >= 5 which becomes 10 >= 5 which is true.
15x + 30y <= 300 becomes 15 * 3 + 30 * 7 <= 300 which becomes 45 + 210 <= 300 which becomes 255 <= 300 which is also true.