# Linear Planning & Mixed Integer Programming Problems

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Three different types of products can be produced. The sales prices, variable production cost, processing times and maximum sales volumes are listed in the following table. The single machine capable of producing any of the products is available for a total of 20,000 minutes.

product 1 2 3
sales price [€/unit] 4.00 6.00 6.00
production cost [€/unit] 1.50 3.00 2.00
processing time [min/unit] 1.25 1.00 4.00
max. sales volume [units] 10,000 13,250 20,000

a) Formulate a linear planning model to determine production volumes of the products with the objective to maximize total profit margin. Explicitly use the data provided. Define any symbols you might need.
b) Amend your model from part a) for the following situation: the maximum sales volume of products 1 and 2 together (!) could be increased by 2,000 units (again: for both products together!) when launching an image campaign with a cost of 1,500 €.
Be careful to formulate a linear or mixed integer / binary model. Avoid other non-
linearities. Define all additional symbols used. No solution is required, just the model amendments!
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