The following table summarises the key facts about two products, A and B, and three resources Q, R, and S, required to produce them.
Resource Usage
Resource per Unit Produced Amount of Resource
Product A Product B Available
Q 2 1 2
R 1 2 2
S 3 3 4
Profit per unit 3 2
All the assumptions of linear programming hold.
1. Formulate a linear programming model for this problem.
2. Solve this model graphically.
3. Verify the exact value of your optimal solution by solving algebraically for the simultaneous solution of the relevant two equations.