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