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

Let x represent the number of flowering plants and y represent the number of nonflowering plants. Joey wants to have at least twice as many flowering plants as nonflowering plants, then .

He wants to have minimum of 36 plants in his garden, this means that .
Flowering plants sell for $8, and nonflowering plants sell for $5, hence the total cost of plants is C=8x+5y and you should minimize this value.

When 2y=x, 2y+y=36 and y=12, x=24. Point (24, 12) is one of the vertices of the feasible region for this problem (two another vertices lie on the axis).

At (24,12) you have C=8·24+5·12=192+60=252