henrietta is planting a new flower garden. she must have yellow and red rosebushes. let x represent the number of yellow rosebushes and y represent the number of red rosebushes. she wants at least 4 times as many yellow rosebushes as red rosebushes. each yellow rosebush costs $7.50 and each red rosebush costs $4.75. she can spend no more than $125. select all of the constraints for this situation. x>0 x greater than 0 x≥4y x greater than or equal to 4 y y≥4x y greater than or equal to 4 x 7.50x 4.75y≤125 7.5 x plus 4.75 y less than or equal to 125 7.50x 4.75y≥125 7.5 x plus 4.75 y greater than or equal to 125 y>0

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AmitPaswan AmitPaswan · Answer 1 · 2022-09-16T10:59:13-04:00

The constraints that are suitable for the situation are x≥4y , 7.50x+4.75y≤125 , x>0 and y>0 .

In the question it is given that

"x" represent the number of yellow rosebushes.

"y" represent the number of red rosebushes.

The word "at least' means "≥".

So "at least 4 times as many yellow rosebushes as red rosebushes" means x≥4y . (constraint 1)

The number of red or yellow rosebushes cannot be negative .

So , x>0 (constraint 2)

y>0 (constraint 3)

Also ,

the cost of each yellow rosebushes = $7.50

number of yellow rosebushes = x

total cost of yellow rosebushes =7.50x

the cost of each red rosebushes = $4.75

number of yellow rosebushes = y

total cost of yellow rosebushes =4.75y

According to the question ,

she can spend no more than $125 , that means

7.50x+4.75y≤125 ( constraint 4)

Therefore , the constraints that are suitable for the situation are x≥4y , 7.50x+4.75y≤125 , x>0 and y>0 .

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