# Assignment 7.

## Maximum 10 points

In the modern world, every consumer often has to make decisions about replacing old equipment with more energy-efficient alternatives. Consider a city dweller who uses a 60 W incandescent lamp for 100 hours each month. The electricity tariff is 5 rubles/kWh.

The city dweller can buy a more energy-efficient lamp with a power of 12 W, which costs 120 rubles and provides the same light output as the aforementioned incandescent lamp. Alternatively, he can approach an investor (an energy service company) that will install such an energy-saving lamp itself, but in return, the city dweller must pay the company 75% of the resulting cost savings on electricity for 10 months (the tariff payment is made regardless of the method of lamp installation).

(a) If the city dweller plans his expenses only for the next 10 months, will he install the energy-saving lamp himself or approach the investor company?

(b) If the city dweller plans his expenses for the entire service life of a typical energy-saving lamp, what decision will he make?
# Solution and Grading Scheme:

a) Expenses for 10 months when installing an energy-saving lamp independently:

$$
120 \text { rub. }+12 \text { (W) * } 100 \text { (hours) / } 1000 \text { * } 5 \text { (rub./kW*hour) * } 10 \text { (months) = } 180 \text { rub. }
$$

Expenses for 10 months when turning to an energy service company:

$$
(12+(60-12) * 0.75)(W) * 100 \text { (hours) / } 1000 \text { * } 5 \text { (rub./kW*hour) * } 10 \text { (months) = } 240 \text { rub. }
$$

Thus, the most cost-effective of the alternative options considered is to install the energy-saving lamp independently.

Full correct solution - 6 points. Only one option correctly calculated - 3 points.

b) The expected service life of a typical lamp is more than 10 months. Since after 10 months, you only need to pay for electricity consumption, as in part a), it will be more cost-effective to install the lamp independently.

Justification (including calculations) 4 points

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