Mathematic. models in economics and management. Themes 2.3

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Objective 1.
The table lists the specific information in terms of value (rub.) Of cross-sectoral balance of the Komi Republic for 1999 Get these data matrix technology coefficients vector of the final consumption and the total added product produced by these sectors of the economy of the Republic of Komi.
Table 1.1
Initial data

Which industries provides the greatest relative pribavoch-tion product?
Is the model presented Leontief productive?

Objective 2.
Private enterprise can produce five different products in an arbitrary ratio. With the release of each type of product involved three machines. Production Process parameters are given in the table.
The cost of salary is $ 4 per hour for machinists 1 and 2 machines and $ 3 per hour for the machine operator on the third machine. Resource working time of each machine is 128 hours per week.
a) Find a product roadmap providing the maximum profit of the company.
b) What price the firm can pay for getting an extra hour working time machine 2?
c) In how many dollars should change selling price of product A, before changing the optimal production plan?

Task 3.
Broker Exchange client instructed to place $ 100,000. US-tion on the funds market in order to obtain the greatest possible profit from the invested capital. The choice is limited to the purchase of shares of four possible types A, B, C, D, which allows to receive an annual income of 6, 8, 10, and 9% per annum of the embedding-zhennoy amount. In order to ensure the liquidity of at least 25% of the total amount of capital should be placed in stock D. Client at least half of the capital must be invested in shares of A and B. In view of the forecast to changing situations in the future, it is considered advisable to invest in stocks with no more than 20 percent of the capital. Finally, taking into account the possible change in the law in the action and a prudent invest at least 30% of the capital. Form a portfolio that provides the highest revenue.

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