Question #51725

A manufacture is to market a new fertilizer which is to be a mixture of ingredients A and B. The properties of the two ingredients are as give on the table below

Properties of the ingredients Cost per kg

Bone meal Nitrogen Lime Phosphate

Ingredients A 20% 30% 40% 10% 12

B 40% 10% 50% 50% 8

It has been decided that the fertilizer will:

i. Be sold in bags containing 100 kilograms

ii. Be containing at least 15 kilograms of nitrogen

iii. Must contain at least 8 kilograms of phosphate

iv. Must contain at least 25 kilograms of bone meal

The manufacturer wants to meet the above requirements at minimum cost possible.

Required

Develop a linear program and hence find the optimal solution for the problem.

Properties of the ingredients Cost per kg

Bone meal Nitrogen Lime Phosphate

Ingredients A 20% 30% 40% 10% 12

B 40% 10% 50% 50% 8

It has been decided that the fertilizer will:

i. Be sold in bags containing 100 kilograms

ii. Be containing at least 15 kilograms of nitrogen

iii. Must contain at least 8 kilograms of phosphate

iv. Must contain at least 25 kilograms of bone meal

The manufacturer wants to meet the above requirements at minimum cost possible.

Required

Develop a linear program and hence find the optimal solution for the problem.

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