A manufacturer produces 3 chemicals: A, B and C. These chemicals are produced in two production processes: 1 and 2. Running process 1 for an hour costs $4 and produces 3 units of A, 1 unit of B and 1 unit of C. Running process 2 for an hour costs $1 and produces 1 unit of A and 1 unit of B. To meet customer demands, at least 10 units of A, 5 units of B, and 3 units of C must be produced daily.
a) Formulate a Linear Programming model to determine a schedule that will minimize the cost for the company. Clearly define your decision variables, objective function and constraints
b) Find the optimal solution using the graphical method
c) Determine graphically how much the cost per hour for process 1 must change before the optimal solution changes?
d) Determine graphically how much the cost per hour for process 2 must change before the optimal solution changes?
e) What would be the effect on the optimal solution if the cost per hour for process 1 changes to $3
f) Determine graphically by how much the demand for one of the three chemicals needs to change and determine which chemical it is before the optimal solution will utilize only one of the two processes?