A farmer plans to mix two types of food to make a mix of low-cost feed for the animals on his farm. A bag of food A costs $10 and contains 40 units of proteins, 20 units of minerals, and 10 units of vitamins. A bag of food B costs $12 and contains 30 units of proteins, 20 units of minerals, and 30 units of vitamins. Solve a linear programming model that helps you decide on the amount of bags of food A and B that should be consumed by the animals each day to meet the minimum daily requirements of 150 units of proteins, 90 units of minerals, and 60 units of vitamins at a minimum cost? Based on your solutions, which of the following is true.

a) The optimal solution is that 3.75 bags of food A and 0.75 bags of food B are needed to satisfy the minimum daily requirements in terms of proteins, minerals, and vitamins.

b) The lowest possible cost is $46.50.

c) The shadow price of the ‘minerals constraint’ is 0.45”, which stands for that if an extra unit of minerals is available, it will increase the value of the objective function by this amount.

d) There is a surplus of 22.5 units of vitamins.