Originally Posted by

**bennyluk** This is my homework, I have try my best to solve it, but It seems very hard to find out the x1, x2, and x3. Can anyone help me? Thank you very much!

Can anyone just write down the constraints or tips, I hope I can do the rest..Thx!

Tasty Cereal Pty Limited makes three types of cereals: Regular, Deluxe and Super using four different ingredients. The selling prices (per kg) for Regular, Deluxe and Super cereals are 6.50, 7.90 and 8.90 respectively. Availability, costs and usage of the ingredients are given in the table below.Tasty Cereal Pty Limited makes three types of cereals: Regular, Deluxe and Super using four different ingredients. The selling prices (per kg) for Regular, Deluxe and Super cereals are 6.50, 7.90 and 8.90 respectively. Availability, costs and usage of the ingredients are given in the table below.

Ingredient| Availability (kg/day)|Fat (units/kg) | Protein (units/kg) | Calories per kg | cost (dollar/per kg)

1 |1800 |12 |25 |180 |3.90

2 |2500 |9 |32 |220 |4.30

3 |2200 |15 |28 |160 |3.20

4 |1900 |18 |20 |130 |2.90

The Regular Cereals must have at most 18 units of fat, at least 24 units of protein and between 140 and 175 calories per kg. The Deluxe Cereals must have at most 15 units of fat, at least 27 units of protein and between 160 and 190 calories per kg. The Super Cereals must have at most 12 units of fat, at least 30 units of protein and between 180 and 200 calories per kg. It iscompany policy that at least 30% production should be Regular Cereal and no more than 25% is Super Cereal.

Develop a linear programming model for the above problem, Allocation of each type of ingredient to produce each type of cereal and Production levels of each type of cereal.

Cheers

Benny