Joey is buying plants for his garden. he wants to have at least twice as many flowering plants as nonflowering plants and a minimum of 36 plants in his garden. flowering plants sell for $8, and nonflowering plants sell for $5. joey wants to purchase a combination of plants that minimizes cost. let x represent the number of flowering plants and y represent the number of nonflowering plants. what are the vertices of the feasible region for this problem?

A vertex in geometry is the intersection of two or more curves, lines, or edges. Vertices are frequently represented by the letters P, Q, R, or S. The intersection of two lines to form an angle, as well as the corners of polygons and polyhedra, are vertices according to this definition.

He desires at least two times as many flowering plants as non-flowering ones.

According to the given information:

the amount of blossoming plants be = x

the number of non-flowering plants be. = y

The question states

Assuming the following circumstance, inequality is:

x ≥ 2y = 0 ..............(1)

Additionally, the inequality must be reflected by at least as many flowers in the garden as:

x + 2y ≥36 .................(2)

The price of x blooming plants will be. = 8x

the cost of y nonflowering plants be = 9y

Additionally, in order to prevent inequality, he must reduce costs.

the lowest price

Now,

Ones that meet the requirements (1) and are feasible (2).

In order to overcome constraints (1) and (2), we get

using equation (1)'s value as the value for equation (2)

2y + y = 36

3y = 36

y = 36/3

y = 12

then

x = 24

With Equation (1) & (1) once more solved, we obtain x = 0 & y = 36.

Hence,

The Feasible region's vertices are as follows.

(24,12)(0,36)

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