3. Maria Ivanovna decided to use the services of an online clothing store and purchase summer clothing: trousers, a skirt, a jacket, and a blouse. Being a regular customer of this store, Maria Ivanovna received information about two ongoing promotions. The first promotion allows the customer to use an electronic coupon worth 1000 rubles, which can cover no more than $15 \%$ of the cost of the ordered items. The second promotion allows the customer to get every third item, which has the lowest price, for free when making a purchase. The online store offers the option to pick up the items from any pickup point located in the city where Maria Ivanovna lives, or to have them delivered to any address within the city. Delivery from a pickup point costs the customer 100 rubles, while delivery to a specified address costs 350 rubles if the order amount does not exceed 5000 rubles. If the order amount exceeds 5000 rubles, delivery to the specified address is free. Maria Ivanovna has selected the following set of clothing:

| Trousers | 2800 rubles |
| :--- | :--- |
| Skirt | 1300 rubles |
| Jacket | 2600 rubles |
| Blouse | 900 rubles |

a) What is the smallest amount of money Maria Ivanovna will have to pay for her purchases, including delivery, if the promotions of the online store cannot be combined (used simultaneously)?

b) Explain why Maria Ivanovna's actual expenses for this purchase in this online store may be higher than the monetary amount found in the previous question. (20 points)
Solution:

(a) Maria Ivanovna can make one purchase, using only one of the promotions, or she can "split" the selected items into two purchases, using both promotions in this case.

Let's consider all possible options:

1) One purchase. In this case, Maria Ivanovna can save either 900 rubles by using the "third item free" promotion, or $((2800+1300+2600+900) * 0.85=1140>1000) \quad 1000$ rubles by using the coupon. Delivery will be free in both of these cases. Thus, if Maria Ivanovna buys all the items in one purchase, the maximum savings will be 1000 rubles, and the cost of the purchase will be $2800+1300+2600+900-1000=6600$ rubles.
2) Two purchases. The most expensive of the cheapest third items in the purchase can be either the skirt or the blouse. If the free item is the skirt, then the coupon should be used for the blouse and it should be ordered as a separate purchase. If the free item is the blouse, then the coupon is most profitable to use for the most expensive item - the trousers.

Let's consider the cost of each such purchase.

1st option:

Cost of purchase 1 (trousers, jacket, skirt) = 2800 + 2600 = 5400 rubles. Delivery of this purchase will be free.

Cost of purchase 2 (blouse) $= 900 * 0.85 = 765$. Delivery of this purchase will cost a minimum of 100 rubles for self-pickup.

Total cost of the option: $5400 + 765 + 100 = 6265$

2nd option:

Cost of purchase 1 (jacket, skirt, blouse) = 2600 + 1300 = 3900 rubles. Delivery of this purchase will cost a minimum of 100 rubles for self-pickup.

Cost of purchase 2 (trousers) $= 2800 * 0.85 = 2380$. Delivery of this purchase will cost a minimum of 100 rubles for self-pickup.

Total cost of the option: $3900 + 2380 + 200 = 6480$

Thus, Maria Ivanovna will spend the least amount if she orders two purchases from the online store, one of which will include trousers, jacket, and skirt, and the other - blouse. The cost of such a purchase, including delivery, will be 6265 rubles.

(b) Attention should be paid to at least two main points that can increase the actual cost of the purchase for Maria Ivanovna.

1) The conditions of self-pickup imply that Maria Ivanovna (or the person she entrusts to pick up her order) will spend time and, possibly, money to get to the pickup point. Despite the low cost of this delivery method, the pickup point may be far from the customer. Considering this fact, many people choose delivery to the address specified by the customer, and some may even prefer (in this case) not to split the purchase into two, but to buy all the selected items in one purchase.
2) When placing two purchases instead of one, the customer will also spend more time, the cost of which for him may exceed the benefit of "double" order placement.

Grading criteria (total 20 points):

(a) (total 15 points)

The idea of dividing orders into 1 or 2 purchases is present - 2 points.

Explicit monetary expenses for 1 purchase are correctly calculated - 3 points.

Explicit expenses for 2 purchases are correctly calculated - 4 points for each option.

Comparison is made and the correct answer about the lowest cost of orders is given - 2 points.

A penalty for each arithmetic error is 1 point. However, in the case of a conceptually correct approach to the solution, the penalty for arithmetic errors, if their number exceeds 1 error in each critical section, cannot exceed 50% of the maximum score assigned to it.

(b) (total 5 points)

The idea that implicit (opportunity) costs of purchasing items in an online store are not taken into account is present - 2 points.

At least 2 examples of implicit costs are provided - 3 points.