10 problems in applied mathematics

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Uploaded: 04.09.2013
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+ Excel

(N = 3 - the last digit of the record book)
Objective 1
In the confectionery factory before the New Year arrived orders for gift baskets of sweets from the shops. Possible variations sets, their cost and inventory are shown in the table.
Name of chocolates candies in a set weight, kg Stocks candy kg
A B C
Snickers 0.3 0.2 0.4 2400
Mars 0.2 0.3 0.2 2800
Bounty 0.2 0.1 0.1 2000
Price, rubles. 75 65 77
Determine the optimal number of gift sets, ensuring maximum revenue from the sale.

Task 2
Standards production costs of different types of pizza, the amount of resources and the cost given in table
Products Standards manufacturing costs of 100 pieces. Pizza kg Stocks products, kg
assorted mushroom salami
Mushrooms June 7 August 23
Sausage 2 May 21 August
Dough August 10 June 22
Price per 100 pcs., Ths. Rub. 9 May 6
Determine the optimal number of pizzas, ensuring maximum revenue from sales.

Objective 3
Define the structure of food for catering companies, providing maximum income, based on the specified standard costs of products on first and second courses, in the following table
Resources Normative overhead, 100 kg of food planned fund resources
1st 2nd meals meat fish 2nd 2nd 2nd dairy Other
Meat, T 4 8 0 0 43 3.8
Fish t 0 10 2.5 0 0 28
Vegetables, t 2 3 0 3.2 4.6 24
Flour, groats, poppy-tron products, t 2.1 2.6 2.3 2.8 0 23
Milk, 6.5 l 0 0 21 - 50000
Income rubles. 2 1.3 1.5 0.3 1.7

Task 4
Make the cheapest option 1 ton of feed mixture in accordance with the requirements given in the table
Nutrients Nutrient content,% Claims% by weight
Dry alfalfa meal bard Fishmeal Soybean Meal
Protein 17 28 60 45 At least 35
Fats 5 5 7 0.5 At least 1.5
Fiber 25 April 3 6.5 Not more than 8
Price, rubles. 1 m 700 900 1500 1000

Objective 5
By prescription patient must go to diet and consume season nutrients contained in fruits, in the amounts indicated in the table.
Substances nutrient content in 1 kg of fruit consumption rates r
Strawberry apples currants
A1 3 2 1 33
A 2 1 3 4 67
A3 0 0 5 43
A4 1 1 50 0
Price, rubles. per kg. 50 40 30
Determine how many of each type of fruit you need to buy to fulfill the prescription of a doctor with a minimum cost.

Additional information

Task 6
Broker Exchange client instructed to place 1000000 dollars. US stock market. We need to create a portfolio of securities to maximize interest on invested capital. The choice is limited to four possible objects of investments - stocks A, B, C, D, which allow an income of, respectively, 9, 11, 7, and 9% per annum of the deposit amount. The client requested at least half of the investment put in stocks A and B. In order to ensure the liquidity of at least 25% of the total amount of capital should be placed in stock D. Given the forecast for a change in the situation in the future, action C can invest no more than 20% of the capital . Specifics of tax points to the need for investments in shares A is not less than 30% of the capital.
Determine the distribution of investment capital, ensuring maximum revenue.

Target 7
From point A to point B on a daily basis sent ambulances and passenger trains. Cash wagons of different types, from which you can every day to complete the data of the train and the number of passengers who fit into each of the vehicles listed in the table
Wagon Number of cars in the train number of passengers cars Park
Soon passenger
Luggage 1 1 0 15
Post 1 0 0 11
Reserved seats 8 May 58 78
Compartment 4 June 40 67
Soft 3 1 32 26
Determine
1) the number of ambulances and passenger trains, where the number of passengers reaches a maximum;
2) The optimal number of trains for the case when the railway can not miss more than six passenger trains.

Target 8
The Institute received grants for the implementation of five research projects. As a scientific project leaders considered five nominations scientists. Every scientist to estimate the time it needs to implement the project. The table below shows the times
12 7 7 8 12
August 12 6 7 9
14 7 11 7 6
12 9 6 5 6
13 9 7 12 8
The length of time given in months. Required choose a leader for each project so that the total time of all projects has been minimal.

Target 9
Trading company sells products in five different cities, the purchasing power of residents is estimated at 153, 170, 197, 400, 250 heads. u To implement the company has five sales agents, each of which it sends to one of the cities. The professional level of agents is different; the proportion of goods sold by agents presented table
Cities share of goods sold sales agent
1 2 3 4 5
1 0.3 0.2 0.3 0.1 0.2
2 0.3 0.3 0.4 0.5 0.2
3 0.2 0.3 0.6 0.3 0.4
4 0.3 0.4 0.4 0.2 0.3
5 0.4 0.2 0.4 0.1 0.1
As the spread of sales agents on the cities, the firm has received the maximum revenue from the sale?

Target 10
The company "Union" provides delivery of video and audio cassettes from four warehouses. The stock of cassettes, as well as the volume of orders and shipping rates are presented in Table
Shops Warehouses Stocks, thousand. Pieces.
1 2 3 4
Warehouse 1 5 4 6 3 120
Warehouse 2 5 3 4 5240
Warehouse 3 3 2 3 3 80
Warehouse 4 4 \u200b\u200b4 4 3 60
Orders thousand units 190 170 110 30
Determine the volume of traffic, ensuring their minimum costs.

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