In Lecture 3, we talked about the formulation of a linear programming problem. In this question, you are asked to formulate a linear programming problem.

Scenario: A company produces two products (X and Y). There are two machines (A and B) in this company. 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 maximise the combined sum of the units of X and the units of Y in stock at the end of the week.

Formulate the above problem of deciding how much of each product to make in the current week as a linear program.

1. Write down the unknown variables
2. Write down the objective function
3. Write down the constraints
4. Use the ISO-profit line method to solve the above problem.