# Task 3. (8 points)

In the Sidorov family, there are 3 people: the father works as a programmer with an hourly rate of 1500 rubles. The mother works as a hairdresser at home and charges 1200 rubles per haircut, which takes her 1.5 hours. The son tutors in mathematics and earns 450 rubles per academic hour (45 minutes). Every day, the family needs to prepare food, walk the dog, and go to the store. The mother spends 2 hours preparing food, the father 1 hour, and the son 4 hours. Walking the dog takes 1 hour for any family member. A trip to the store takes 1 hour for the father, 2 hours for the mother, and 3 hours for the son. In addition, each family member sleeps for 8 hours and spends another 8 hours on rest and personal matters.

What is the maximum amount of money the family can earn in one day?
# Solution

In this problem, there are 2 possible interpretations, both of which were counted as correct.

In one case, it is assumed that 8 hours are spent on work on average over the month, in the other that no more than 8 hours are spent on work each day.

## First Case:

1) Determine the hourly wage for each family member. (2 points)

a) Father = 1500 rubles per hour

b) Mother = 1200 / 1.5 = 800 rubles per hour
c) Son = 450 / 0.75 = 600 rubles per hour

2) Calculate how much money the family will lose for each mandatory task depending on who does it. (1 point for each sub-item, total 3 points)

a) Cooking: father - 1500 rubles, mother - 1600 rubles, son - 2400 rubles.

Therefore, the father cooks and spends 1 hour on it.

b) Walking the dog: father - 1500 rubles, mother - 800 rubles, son - 600 rubles.

Therefore, the son walks the dog and spends 1 hour on it.
c) Going to the store: father - 1500 rubles, mother - 1600 rubles, son - 1800 rubles.

Therefore, the father goes to the store and spends 1 hour on it.

3) Calculate the final earnings of each family member: (3 points)

a) Father: 1500 * (24 - 8 - 8 - 1 - 1) = 9000 rubles.

b) Mother: 800 * (24 - 8 - 8) = 6400 rubles.

c) Son: 600 * (24 - 8 - 8 - 1) = 4200 rubles.

d) Total: 9000 + 6400 + 4200 = 19600 rubles.

Answer: 19600 rubles

## Second Case:

1) The number of hours each family member can spend on work or household chores per day: 24 - 8 - 8 = 8 hours.
2) Estimate the maximum income of each family member assuming they do not do household chores (2 points):

a) Father: 1500 * 8 = 12000 rubles.

b) Mother: 1200 * 5 = 6000 rubles + 30 minutes of free time.

c) Son: 450 * 10 = 4500 rubles + 30 minutes of free time.

3) Calculate the lost income from each type of activity (3 points, 1 point for each type of work):

a) Cooking: father - 1500, mother - 1200 (if she didn't go to the store) or -2400 (if she did go to the store), son - 2250.

b) Going to the store: father - 1500, mother - 1200 (if she didn't cook) or -2400 (if she did cook), son - 1800.

c) Walking the dog: father - 1500, mother - 1200, son - 450.

4) Choose the smallest losses: the father and mother cook and go to the store (it doesn't matter who does what, but each does one thing), the son walks the dog (2 points for correctly determining the tasks for each family member).
5) Thus, the maximum earnings: 12000 - 1500 + 6000 - 1200 + 4500 - 450 = 19350 rubles (1 point)

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