A chemical company manufactures three chemicals: A, B, and C. These chemicals are produced via two production processes: 1 and 2. Running process 1 for an hour costs $4 and yields 3 units of A, 1 unit of B, and 1 unit of C. Running process 2 for an hour costs $1 and yields 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) Please write down the standard (mathematical) LP model for solving this problem.
b) Find optimal solutions (daily production plan) that minimize the total daily costs while meeting daily demands.