The code for this example is found in the WhiskasModel2. That kilogram is made up of three parts - ingredient 1, ingredient 2 and filler so let: When there is a choice, it is better to allow slack in a constraint as this provides maximum flexibility for other constraints. The optimised objective function value is printed to the screen, using the value function.

This ensures that the number is in the right format to be displayed. Note here this this optimal solution is not unique - other variable values, e.

Formulate the Objective Function For the Whiskas Cat Food Problem the objective is to minimise the total cost of ingredients per can of cat food. That is, the left hand side of the equation units of measurement must be the same as the right hand side units of measurement.

This inequality is written: Note that I made this constraint an inequality rather than a strict equality. Each general patient needs 2 hours of surgery time and 2 hours of therapy. In this case, note that the right hand side units of measurement are 1, gallons.

Both of these will be worked by the software in Module 6. To meet the nutritional analysis requirements, we need to have at least 8g of Protein per g, 6g of fat, but no more than 2g of fibre and 0.

Here, management must be very careful to precisely articulate what is to be optimized. The status of the solution is printed to the screen print "Status: Production planning problem A company manufactures four variants of the same product and in the final part of the manufacturing process there are assembly, polishing and packing operations.

Generally, when variable costs and revenues are known, the firm would like to determine that production schedule which maximizes profit contribution, so as not to sub-optimize with a production schedule.

This is standard linear programming convention, and this is how the equation will be entered into The Management Scientist. You will notice that there is no assignment operator such as an equals sign on this line. Thus the objective function is simply entered and assigned a name: Fortunately, there are algorithms which quickly determine the most interesting of these many solution: For each variant the time required for these operations is shown below in minutes as is the profit per unit sold.

We must formally define our decision variables, being sure to state the units we are using. Each orthopedic patient needs 4 hours of surgery and 12 hours of therapy. One kg of feed mix must contain a minimum quantity of each of four nutrients as below: It is suggested that you repeat the exercise yourself.

It has four parameters, the first is the arbitrary name of what this variable represents, the second is the lower bound on this variable, the third is the upper bound, and the fourth is essentially the type of data discrete or continuous.

The limitations on these variables greater than zero must be noted but for the Python implementation, they are not entered or listed separately or with the other constraints. The problem data is written to an. We could try a few more, always trying to increase profit contribution subject to meeting the constraints.

The constraint is logically entered after this, with a comma at the end of the constraint equation and a brief description of the cause of that constraint: After the problem is formulated, we proceed to its solution.

Since the can is g, these percentages also represent the amount in g of each ingredient included. Note that these percentages must be between 0 and Another important note at this point is that this constraint has units of measurement in gallons, whereas the first two constraints had units of measurement in units of production.

This will give us the weight in g of each ingredient: It is best to right this constraint exactly as the word problem presents the ratio and proportion: Second, this is a linear algebraic equation with each decision variable raised to the first power no squared terms, for example.

The next constraint in the word problem concerns a general inventory constraint: So, multiple both sides of the equation by B, and move the decision variables to the left hand side: Identify the Decision Variables For the Whiskas Cat Food Problem the decision variables are the percentages of the different ingredients we include in the can.

Thus, you might suggest leaving out this constraint. We will first define our decision variables: The stated nutritional analysis requirements are met.Provides more worked examples of how to set up and solve word problems involving linear programming; includes an example with three items to account for.

Search. Return to the Lessons Index | Do the Lessons in Order | Get What is the optimal blend? Blending or Mixing Problem Another classic problem that can be modeled as a linear program concerns blending or mixing ingredients to obtain a product with certain characteristics or properties.

Finished product blending. Refinery fuel blending.

Importing feedstocks to meet product demand. Exporting surplus refinery streams to other refineries. The refinery LP model, in fact, is simply a set of data tables in the form of spreadsheets that are converted into a matrix using special programming languages.

Abstract: A Stochastic non-linear optimization model using Quadratic Programming (QP) is presented for a hypothetical blending type problem in mining industry. Microsoft Excel Solver is used to develop the model for a three-seam coal mine.

This lesson contains solutions to assorted Linear Programming Word Problems.

QUESTION NUMBER 2 Fred's Coffee sells two blends of beans: Yusip Blend and Exotic Blend. A drug company produces the drug NasaMist from four chemicals. Today, the company must produce pounds of the drug.

The three active ingredients in NasaMist are A, B, and C. By weight, at least 8% of NasaMist must consist of.

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