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Определение максимальной величины дохода при выпуске двух видов однотипной продукции
Юридическая форма предприятия и ее капитал

Определение максимальной величины дохода при выпуске двух видов однотипной продукции. Графический метод линейного прогнозирования.

Условия задачи.

Компания производит два однородных продукта – две версии корпоративной информационная система для автоматизации документооборота предприятия и управления его работы. Версия Full содержит полный комплект функциональных возможностей программного продукта и стоит $25 тыс. Версия Lite обладает более только основным набором функций программного продукта, наиболее  необходимых пользователю, и стоит соответственно меньше -$20 тыс. Также производство этих двух версий отличается по времени и по количеству задействованных в разработке программистов. Для производства версии Full требуется 3 дня и 2 программистов, Lite - 2 дня и 4 программистов. Ограничения: в компании работают 32 программистов по 24 рабочих дня в месяц. Учитывая ограничения на время, людские ресурсы и неотрицательность, необходимо выяснить, сколько продукции каждого вида следует производить ежемесячно, если цель компании максимизация ежемесячного дохода.

Определение переменных. Целевая функция.

1) Определим переменные:

Full = f единиц/месяц

Lite = l единиц/ месяц

2) Определим цели и ограничения:

Р доход max (максимальный фонд) – 24 дн./месяц; V max (количество задействованных программистов) – 32 чел./месяц.

3) Целевая функция задачи:  P = 25f + 20l $/месяц

4) Определим ограничения через переменные:

а) ограничения на время производства работы:  3f + 2l ≤ 24

б) ограничение на количество задействованных людей:  2f + 4l ≤ 32

в) фирма не производит отрицательного количества продукции:  f, l ≥ 0

Формулировка задачи через переменные.

Максимизировать  P = 25f + 20l ($/месяц)

при ограничениях         3f + 2l ≤ 24

                                       2f + 4l ≤ 32

                                       f, l ≥ 0

Графическое решение задачи.

а) Ограничение на время работы:

3f + 2l = 24, f = 0 и l = 0.

Получаем f = 8 и l = 12:

img2

б) Ограничения на количество задействованных людей:

2f + 4l = 32, f = 0 и l = 0.

Получаем f = 16 и l = 8:

img3

в) Ограничение на неотрицательность:

f ≥ 0 и l ≥ 0:

img4

г) Поиск оптимального решения:

     3f + 2l = 24

     2f + 4l = 32

Получаем f = 4 и l = 6:

img5

Определение максимального дохода при заданных ограничениях

В результате решения задачи графическим методом была получены координаты точки “А”: f = 4  и l = 6. Подставив эти значения в формулу задачи, определим максимальный доход:

Рmax = 25f + 20l = 25•4+ 20•6 = 220 тыс. $/ мес.

Таким образом, чтобы получить при заданных ограничениях максимально возможный доход в $220 тыс. в месяц, компания должна производить 4 единицы продукции Full и 6 единиц продукции Lite. При таких объемах выпуска продукции максимально используется время нагрузки и количество работников. В этом случае остаток ресурса и резервный запас продукта отсутствуют.

Заключительная часть

После проведенных в курсовой работы расчетов можно сделать вывод о том, что создание малого предприятия по изготовлению и сбыту программного продукта для телекоммуникаций производственной мощностью 140 экземпляров в год, может принести прибыль, если грамотно организовать производство. Такой вывод можно сделать исходя из данных, полученных в результате  составления  финансового плана:

  • прогноз дохода предприятия за первый год работы составит 1400000$;

  • составленные сметы оценки стоимости основных и оборотных  средств, ежемесячных расходов и наличная смета для оценки потребностей в денежных средствах представляют данные о необходимых денежных средствах;

  • график порога рентабельности показывает, что предприятие будет безубыточным при производстве более 62 продуктов в год;

  • отчет о прибылях и убытках предприятия показывает, что прибыль предприятия за первый год работы составит 60000$; составлен баланс на начало и конец первого года  работы предприятия;


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