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Further Mather decision linear programming

Helppp can someone explain why the inequality is 3y >/ 2z and not 2y</ 3z

Ben is a wedding planner. He needs to order flowers for the weddings that are taking place next month. The three types of flower he needs to order are roses, hydrangeas and peonies.
Based on his experience, Ben forms the following constraints on the number of each type of flower he will need to order.
At least three-fifths of all the flowers must be roses.
For every 2 hydrangeas there must be at most 3 peonies. The total number of flowers must be exactly 1000
The cost of each rose is £1, the cost of each hydrangea is £5 and the cost of each peony is £4 Ben wants to minimise the cost of the flowers.
Let x represent the number of roses, let y represent the number of hydrangeas and let z represent the number of peonies that he will order.
(a) Formulate this as a linear programming problem in x and y only, stating the objective function and listing the constraints as simplified inequalities with integer coefficients.
Ben decides to order the minimum number of roses that satisfy his constraints(7)
Original post by Student1#
Helppp can someone explain why the inequality is 3y >/ 2z and not 2y</ 3z
Ben is a wedding planner. He needs to order flowers for the weddings that are taking place next month. The three types of flower he needs to order are roses, hydrangeas and peonies.
Based on his experience, Ben forms the following constraints on the number of each type of flower he will need to order.
At least three-fifths of all the flowers must be roses.
For every 2 hydrangeas there must be at most 3 peonies. The total number of flowers must be exactly 1000
The cost of each rose is £1, the cost of each hydrangea is £5 and the cost of each peony is £4 Ben wants to minimise the cost of the flowers.
Let x represent the number of roses, let y represent the number of hydrangeas and let z represent the number of peonies that he will order.
(a) Formulate this as a linear programming problem in x and y only, stating the objective function and listing the constraints as simplified inequalities with integer coefficients.
Ben decides to order the minimum number of roses that satisfy his constraints(7)


Consider the single item "2 hydrangeas", and lets call it h - that is the number of pairs of hydrangeas..
Similarly, consider the single item "3 peonies", and lets call it p - that is the number of triplets of peonies.

So, the requirement is h >= p

Now h =y/2, and p = z/3

So, y/2 >= z/3

And rearrange.
Reply 2
Original post by ghostwalker
Consider the single item "2 hydrangeas", and lets call it h - that is the number of pairs of hydrangeas..
Similarly, consider the single item "3 peonies", and lets call it p - that is the number of triplets of peonies.
So, the requirement is h >= p
Now h =y/2, and p = z/3
So, y/2 >= z/3
And rearrange.


Ahh thank you!

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