Doll therapy is one way Alzheimer's disease caregivers ease anxiety and bring joy to loved ones with dementia. CVS retail stores in the USA plan to introduce this doll into their product portfolio. One of the dolls, which is very famous in this segment, is called 'TalktoMe.' CVS stores want to introduce them during the Holiday Season. The supplier offers voice modules for two different languages: Spanish and English. The supplier plans to assemble the specific language voice module at the factory and ship the fully assembled doll, with the language module built-in, to CVS.

Irrespective of the language setting, a doll's manufacturing cost is $60 (including the voice module), and the wholesale price (i.e., the price at which CVS buys the doll from the supplier) is $100. The retail price (i.e., the price at which CVS sells the doll to the customer) is $250. CVS estimates that any unsold inventory of dolls can be sold-off (salvaged) for a discounted price of "90% off" of the retail price per doll.

After researching potential customer demand, CVS anticipates that the English-speaking dolls will sell more than the Spanish-speaking dolls. CVS estimates that the demand for English-speaking dolls follows a Normal distribution with a mean of 2500 units and a standard deviation of 600. For Spanish-speaking dolls, the demand is normally distributed with a mean of 1200 and a standard deviation of 300. You can assume that the demand for the products is independent of each other. The dolls are made in Mexico, and CVS must place the order well before the Holiday Season.

Question 1

How many units of each doll (English and Spanish) should CVS maximize the expected profit? What is CVS's expected profit in this case? What is the supplier's profit in this case?

Question 2

Now the supplier and CVS agree on a revenue-sharing agreement for the doll. Once CVS sells a doll, 14% of the revenue they make (i.e., 14% from the $250 retail price of each doll sold) is shared with the supplier. The supplier, however, only receives 14% of the revenue of dolls sold during the season - it does receive any share of the revenue CVS makes from leftover dolls that are salvaged for a deep discount.

You can assume that the supplier always manufactures on a build-to-order basis. This means that the supplier always produces precisely the order quantity requested by CVS, with no inventory leftover or unfulfilled demand occurring at the supplier's end.

Under this agreement, the supplier agrees to a reduced wholesale price of $70 per doll. The cost of manufacturing for the supplier remains $60 per doll. The supplier will generate additional profit from its share of the retailer's revenue.

How many units of each doll (English and Spanish) should CVS now order to maximize the expected profit? Calculate the expected profit for both the supplier and for CVS under this revenue-sharing agreement.

Question 3

Compare the profits for the retailer and the supplier in Questions 1 and 2. What is your explanation for the difference between the profits?