السلام عليكم ورحمة الله

[نورمكة]

انا عضو جديد اتمنى منكم المساعدة عندي سوال مو عارفة احلو يارت الي يعرف الحل لا يبخل عليا وشكرا



1)A company makes two products (X and Y) using two machines (A and B). Each unit of X that is produced requires 50 minutes processing time on machine A and 30 minutes processing time on machine B. Each unit of Y that is produced requires 24 minutes processing time on machine A and 33 minutes processing time on machine B.
At the start of the current week there are 30 units of X and 90 units of Y in stock. Available processing time on machine A is forecast to be 40 hours and on machine B is forecast to be 35 hours.
The demand for X in the current week is forecast to be 75 units and for Y is forecast to be 95 units. Company policy is to maximize the combined sum of the units of X and the units of Y in stock at the end of the week.
• Formulate the problem of deciding how much of each product to make in the current week as a linear program.
• Solve this linear program graphically.
2) Write the algorithm for the initial solution of the transportation problem using one method and trace it.
3) What is the relation between the dual and primal problem give an example.