Question

30 БАЛЛОВ Мобильный оператор «АХ» берёт 1 зед (зед — условная денежная единица) за подключение и 2 зеда за каждую минуту разговора, а мобильный оператор «ОХ» берёт за первую минуту разговора 1 зед, а за каждую следующую на 0,5 зеда больше, чем за предыдущую. Качество обслуживания у обоих операторов одинаковое. 1) Услугами какого оператора выгоднее пользоваться, если каждый день звонить: а) 5 – 6 раз по 7 – 8 минут; б) 10 – 11 раз по 3 – 4 минуты? 2) При какой средней длительности с точностью до минуты ежедневных звонков выгоднее пользоваться услугами оператора «АХ»?

Answer 1

1) АХ - 2 зеда за каждую минуту
ОХ - 1 зеда за первую минуту и за каждые после первой минуты 0,5 зеда.
1) 2 * 7 * 5 = 70 (з.) - 5 раз по 7 минут (АХ)
2) (1 * 1 + 0,5 * 2) * 10 = 20 (з.) - 10 раз по 3 минуты (ОХ)
Ответ: Выгоднее пользоваться мобильным оператором "ОХ".

Answer 2

Mobile Operator Pricing Comparison

To determine which mobile operator is more cost-effective, we need to compare the pricing plans of "AH" and "OH" for different calling scenarios.

According to the information provided, "AH" charges 1 zed for connection and 2 zeds per minute of conversation. On the other hand, "OH" charges 1 zed for the first minute and an additional 0.5 zed for each subsequent minute.

Let's analyze two different calling scenarios:

Scenario A: 5-6 calls per day, each lasting 7-8 minutes In this scenario, we need to calculate the total cost for both operators.

For "AH": - Connection fee: 1 zed - Minutes of conversation: (5 calls * 7 minutes) + (1 call * 8 minutes) = 43 minutes - Cost of conversation: 43 minutes * 2 zeds/minute = 86 zeds

Total cost with "AH": 1 zed (connection fee) + 86 zeds (conversation cost) = 87 zeds

For "OH": - Connection fee: 1 zed - Minutes of conversation: (5 calls * 7 minutes) + (1 call * 8 minutes) = 43 minutes - Cost of conversation: 1 zed (first minute) + (42 minutes * 0.5 zeds/minute) = 22 zeds

Total cost with "OH": 1 zed (connection fee) + 22 zeds (conversation cost) = 23 zeds

Scenario B: 10-11 calls per day, each lasting 3-4 minutes In this scenario, we need to calculate the total cost for both operators.

For "AH": - Connection fee: 1 zed - Minutes of conversation: (10 calls * 3 minutes) + (1 call * 4 minutes) = 34 minutes - Cost of conversation: 34 minutes * 2 zeds/minute = 68 zeds

Total cost with "AH": 1 zed (connection fee) + 68 zeds (conversation cost) = 69 zeds

For "OH": - Connection fee: 1 zed - Minutes of conversation: (10 calls * 3 minutes) + (1 call * 4 minutes) = 34 minutes - Cost of conversation: 1 zed (first minute) + (33 minutes * 0.5 zeds/minute) = 17.5 zeds

Total cost with "OH": 1 zed (connection fee) + 17.5 zeds (conversation cost) = 18.5 zeds

Conclusion

Based on the calculations for both scenarios, it is more cost-effective to use the services of mobile operator "OH" in both cases. The total cost of using "OH" is significantly lower than that of "AH" for the given calling patterns.

Optimal Call Duration for Operator "AH"

To determine the optimal call duration for using the services of operator "AH," we need to find the point at which the cost of using "AH" becomes lower than using "OH."

Let's calculate the cost for different call durations with operator "AH":

- Connection fee: 1 zed - Minutes of conversation: x minutes - Cost of conversation: x minutes * 2 zeds/minute

To find the break-even point, we need to equate the cost of using "AH" with the cost of using "OH" (which is 18.5 zeds, as calculated in Scenario B):

1 zed + (x minutes * 2 zeds/minute) = 18.5 zeds

Simplifying the equation:

x minutes * 2 zeds/minute = 17.5 zeds

x minutes = 17.5 zeds / (2 zeds/minute)

x minutes = 8.75 minutes

Therefore, with a call duration of approximately 8.75 minutes, it becomes more cost-effective to use the services of operator "AH" compared to operator "OH."

Please note that these calculations are based on the given pricing information and assume that the quality of service is the same for both operators.