Problem
Two chemical plants, one at Macon and one at Jonesboro, produce three types of fertilizer, low phosphorus (LP), medium phosphorus (MP), and high phosphorus (HP). At each plant, the fertilizer is produced in a single production run, so the three types are produced in fixed proportions. The Macon plant produces 1 ton of LP, 2 tons of MP, and 3 tons of HP in a single operation, and it charges $600 for what is produced in one operation, whereas one operation of the Jonesboro plant produces 1 ton of LP, 5 tons of MP, and 1 ton of HP, and it charges $1000 for what it produces in one operation. If a customer needs 100 tons of LP, 260 tons of MP, and 180 tons of HP, how many production runs should be ordered from each plant to minimise costs?
For the situation given above:
1) Determine the decision variables.
2) Formulate the situation into a Linear Programming problem
3) Represent the feasible region graphically.
4) Find the optimal solution graphically. How many production runs should be ordered from each plant to minimize costs?
5) Determine the binding and non-binding constraints.