7. You are the owner of a company selling Tesla Model S electric vehicles. The purchase price of one car is 2.5 million rubles. To transport one car across the border, you need to pay customs duties and fees totaling 2 million rubles per car. Monthly office rent is 50,000 rubles, and the total monthly salary of employees is 370,000 rubles. Other monthly expenses, including the import of vehicles, rental of space for storage of imported vehicles, do not depend on the number of vehicles and amount to 180,000 rubles. Your store has received an order for 30 Tesla Model S cars.

a) Determine the minimum possible price of one car (in million rubles) at which you would be willing to accept this order. Assume that all operations related to fulfilling this order can be carried out within one month and that you will not receive any other orders for purchasing cars in this month.
b) A company has appeared in the city selling these cars for 5.3 million rubles each, providing a free charging station worth 400,000 rubles with each purchased car. At what minimum order volume could you compete with this company if charging stations can be freely purchased on a competitive market? (17 points).
# Solution:

a) The sum of monthly costs to ensure the deal is: $(2.5+2) \cdot 30+(0.05+0.370+0.18)=135.6$ million rubles. The average cost per car will be $135.6 / 30=4.52$ million rubles. This is the minimum amount for which the company will be willing to sell one car. If the car's cost is lower, the company will incur losses and it will be more profitable to refuse the order.

b) Let $\boldsymbol{X}$ be the number of cars in the order. Then the average cost per car will be: $[(2.5+2) \cdot \boldsymbol{X}+(0.05+0.370+0.180)] / \boldsymbol{X}$. You will be able to compete only if the average cost per car does not exceed the competitor's price without the cost of the charging station, i.e.,

$[(2.5+2) \cdot X+(0.05+0.370+0.180)] / X \leq 5.3-0.4$, from which we find $X \geq 1.5$. Considering that $X$ is an integer, the minimum number of cars in the order will be 2 units.

Answer: a) 4.52 million rubles; b) 2 units.

## Grading Criteria:

a)

1) Correctly calculated the company's monthly expenses - 3 points
2) Correctly outlined the idea of the minimum price at which the company will be willing to sell a car - 3 points. If there are no justifications, points for this part of the solution are not awarded.
3) Found the minimum price - 2 points

b)

1) Correctly outlined the idea of price comparison - 3 points. If there are no justifications, points for this part of the solution are not awarded.
2) Correctly calculated the average cost per car - 3 points
3) Correctly found the number of cars - 3 points