# Model file for BT-ILO problem 1.15

param n_Prod;	 # No. product types
param ProdAssembly {1..n_Prod};	# assembly hrs per product
param ProdTesting {1..n_Prod};	# testing hrs per product
param ProdRawMatl {1..n_Prod};  # raw materials per product
param Value {1..n_Prod};	# value for each product
param AssemblyHours;
param TestingHours;

var x {1..n_Prod} >= 0;	# x[j] = # of product j made

param OverTimeCost;	# cost per hour of overtime
param MaxOverTime;
var h >= 0;		# hours of overtime assembly	

maximize Profit: sum {j in 1..n_Prod} (Value[j]-ProdRawMatl[j])*x[j] - OverTimeCost*h;

subject to AssemblyCon: sum {j in 1..n_Prod} ProdAssembly[j]*x[j] <= AssemblyHours + h;
subject to TestingCon:  sum {j in 1..n_Prod} ProdTesting[j]*x[j] <= TestingHours;
subject to OTUpperBound: h <=  MaxOverTime;

subject to NoOverTime: h = 0 ;
# This constraint essentially removes the variable h from the model
# To include the overtime option, we need to drop this constraint