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EAE38E - Mathematics for Economists II

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Vyučující: doc. Ing. Ph.D. Tomáš Šubrt

Popisek: Foto variant testu za Math 2

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LP Problem: Essential Conditions
First, there must be limited resources (e.g., a limited number of workers, machines, finances, and material); otherwise there would be no problem, nothing to be sold.
Second, there must be an explicit objective (such as maximize profit or minimize cost). When a single objective is to be maximized or minimized, we can use linear programming. When multiple objectives exist, multi objective programming is used.
Third, there must be linearity (if it takes three hours to make a part, then two parts would take six hours, three parts would take nine hours etc.). Other restrictions on the nature of the problem may require that it be solved by other variations of the technique, such as non-linear programming or dynamic programming.
Fourth, there must be homogeneity (the products are identical, or all the hours available from a worker are equally productive).
Fifth is divisibility (products and resources can be subdivided into fractions). If this subdivision is not possible (such as flying half an airplane or hiring one-fourth of a person), integer programming, can be used
LP: Basic Groups of Applications

1) Product Planning = Finding the minimum-cost or maximum profit production schedule
A manufacturing firm produces two products, A and B. Each of these products must be processed through two different machines. One machine has 24 hours of available capacity, and the second machine has 16 hours. Each unit of product A requires three hours of time on both machines. Each unit of product B requires two hours of time on the first machine and one hour on the second machine. The profit is $8 per unit of product A and $6 per unit of product B, and the firm can sell as many units of each product as it can produce. The objective of the firm is to maximize profits. The problem is to determine how many units of product A a

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Reference vyučujících předmětu EAE38E - Mathematics for Economists II
Reference vyučujícího doc. Ing. Ph.D. Tomáš Šubrt

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