LINEAR PROGRAMMING PROBLEM Minimization with sensitivity analysis

A patient visits a doctor to get treatment for ill health. The doctor examines the patient and advises him to consume at least 40 units of vitamin A and 50 units of vitamin B daily for a specified time period. He also advises the patient that to get vitamin A and vitamin B he has to drink tonic X and tonic Y that have both vitamin A and vitamin B in a proportion. One unit of tonic X consists of 2 units of vitamin A and 3 units of vitamin B and one unit of tonic Y consists of 4 units of vitamin A and 2 units of vitamin B. These tonics are available in medical shops at a cost of birr 3.00 and birr 2.50 per unit of X and Y respectively. Now the problem of patient is how much of X and how much of Y is to be purchased from the shop to minimize the total cost and at the same time he can get the required amounts of vitamins A and B. (use simplex methods for your solution).

Required

1. Develop/Formulate the standardized model for the LP problem
2. Interpret the elements of the optimal solution properly.
3. Identify the shadow prices of the constraints and explain their implication.
4. The decision variable is a matrix with Size X Plant.
5. Determine the Range of feasibility (RoF) of all the constraints.