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. A full list of the topics available in OR-Notes can be found here. At the start of the current week there are 30 units of X and 90 units of Y in stock.

Formulate the problem of deciding how much of each product to make in week 5 as a linear program. Formulate the problem of deciding how much to produce per week as a linear program.

Both machine and craftsman idle times incur no costs. Each unit of Y that is produced requires 24 minutes processing time on machine A and 33 minutes processing time on machine B. J E Beasley OR-Notes are a series of introductory notes on topics that fall under the broad heading of the field of operations research OR.

The available time on machine X in week 5 is forecast to be 20 hours and on machine Y in week 5 is forecast to be 15 hours. For product 2 applying exponential smoothing with a smoothing constant of 0.

Machine time Craftsman time Item X 13 20 Y 19 29 The company has 40 hours of machine time available in the next working week but only 35 hours of craftsman time. The company has a specific contract to produce 10 items of X per week for a particular customer.

They are now available for use by any students and teachers interested in OR subject to the following conditions.

For product 1 applying exponential smoothing with a smoothing constant of 0. Solution Note that the first part of the question is a forecasting question so it is solved below.

Available processing time on machine A is forecast to be 40 hours and on machine B is forecast to be 35 hours.

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 product 1 that is produced requires 15 minutes processing on machine X and 25 minutes processing on machine Y.

We can now formulate the LP for week 5 using the two demand figures 37 for product 1 and 14 for product 2 derived above. Solve this linear program graphically.

Solution x be the number of units of X produced in the current week y be the number of units of Y produced in the current week then the constraints are: The resources need to produce X and Y are twofold, namely machine time for automatic processing and craftsman time for hand finishing.

These products are produced using two machines, X and Y.

Week 1 2 3 4 Demand - product 1 23 27 34 40 Demand - product 2 11 13 15 14 Apply exponential smoothing with a smoothing constant of 0. Formulate the problem of deciding how much of each product to make in the current week as a linear program.

Solution x be the number of items of X y be the number of items of Y then the LP is: Each unit of product 2 that is produced requires 7 minutes processing on machine X and 45 minutes processing on machine Y.

The table below gives the number of minutes required for each item: The demand for X in the current week is forecast to be 75 units and for Y is forecast to be 95 units.Discrete 1 - Decision 1 - Linear programming - optimal solution - shading inequalities - feasible region - Worksheet with 16 questions to be completed on the sheet - solutions included/5(9).

This is a quiz on 'Linear Programming'. There are a total of 41 questions. Answer any 40 questions. Each question carries 2 marks and the total marks are Below are links to many examples on how to formulate and solve optimization problems in linear programming.

Solve Inequalities with Two Variables. Solve Systems of Inequalities with Two Variables. Linear programming - exam questions. Question 1: June Question 2: Jan Question 3: June Show that your answers in part (a) become 2x + y x Formulate Ernesto's situation as a linear programming problem.

On Figure 3, draw a suitable diagram to enable the problem to be solved.

Linear programming example UG exam A company manufactures two products (A and B) and the profit per unit sold is £3 and £5 respectively. Each product has to be assembled on a particular machine, each unit of product A taking 12 minutes of assembly time and each unit of. LINEAR PROGRAMMING: Some Worked Examples and Exercises for Grades 11 and 12 Learners.

Example: A small business enterprise makes dresses and trousers. To make a dress requires graph to answer the following questions: Write down the set of .

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