Could you please help me to solve the task using optimization method?
The factory produces three types of glue. And four types of chemicals are used for its production: starch, gelatin, alum and chalk. The following table presents the consumption (in kilos) of these chemicals to obtain one kilogram of each type of glue and their stock in the warehouse of the factory:
\begin{array} {|c|c|} \hline & \text{Glue 1} & \text{Glue Two} & \text{Glue Three} & \text{Warehouse Stock}\\ \hline \text{Starch} & 0.4 & 0.3 & 0.2 & 20 \\ \text{Gelatin} & 0.2 & 0.3 & 0.4 & 35 \\ \text{Alum} & 0.05 & 0.07 & 0.1 & 7 \\ \text{Chalk} & 0.01 & 0.05 & 0.15 & 10 \\ \hline \end{array}
The cost of each type of glue in the domestic market is: $c_1 = 380$ euro/kg; $с_2 = 430$ euro/kg; $с_3 = 460$ euro/kg; The cost of each type of glue in the foreign market is: $d_1=12$ dollar/kg; $d_2 = 10$ dollar/kg; $d_3 = 8$ dollar/kg. It is required to determine the optimal volume of glue production of each type, providing a maximum of the total cost of the entire batch of glue both in the domestic and foreign markets.
I can't deduce the conditions from this problem if we take $x_i = \text{Glue}_i$
Could you please help me?