Linear Programming - Branch and bound question

Question 5 Delijus Factory produces two types of juices: Orange and Mango assembled in crates of 1000 cartons per crate. The production process of a particular batch involves two stages: processing and bottling. The following table gives the time in hours for each stage, and also the profit in (S$) for each crate. Stages Maximum time (hours per day) Orange (hours) 50 30 1400 processing bottling profit (S$) per crate Mango (hours) 40 50 1600 70 60 Table 05 No unfinished crate can be left overnight. (a) Formulate the Delijus Factory's problem as an integer programming model. (6 marks) (6) Starting from the solution to the continuous problem, use the branch-and-bound method to solve the first two sub-problems which arise. Indicate how the solution would proceed if the branch-and-bound method were to continue. Draw the tree diagram for the solution process so far. Construct a table of your results along the following format. Problem I Problem Solution to Gk solved. Ckx X Current bound Problem to pursue Stored problems (10 marks) Write down the constraints of the above model if the orange type of juice should be at least 60% of the quantity of juice produced Question 5 Delijus Factory produces two types of juices: Orange and Mango assembled in crates of 1000 cartons per crate. The production process of a particular batch involves two stages: processing and bottling. The following table gives the time in hours for each stage, and also the profit in (S$) for each crate. Stages Maximum time (hours per day) Orange (hours) 50 30 1400 processing bottling profit (S$) per crate Mango (hours) 40 50 1600 70 60 Table 05 No unfinished crate can be left overnight. (a) Formulate the Delijus Factory's problem as an integer programming model. (6 marks) (6) Starting from the solution to the continuous problem, use the branch-and-bound method to solve the first two sub-problems which arise. Indicate how the solution would proceed if the branch-and-bound method were to continue. Draw the tree diagram for the solution process so far. Construct a table of your results along the following format. Problem I Problem Solution to Gk solved. Ckx X Current bound Problem to pursue Stored problems (10 marks) Write down the constraints of the above model if the orange type of juice should be at least 60% of the quantity of juice produced