Suppose you have been recently employed as manager of a restaurant and a very important credit card firm offers you a deal that is supposed to raise your sales. The deal proposed is the following: for each customer that uses this company's credit card the second person on the same party eats for half the price.

The restaurant owner is sort of desperate to increase the volume of sales for the restaurant after having lost a little bit more than 20 percent of his customers due to the recent Great Recession. However, he also knows that the economics of the restaurant are not in great shape due to the fact that this is an old restaurant and fixed costs are very high and very difficult to decrease. Thus, giving free meals is not a good way of saving the business.

Your job is to determine a strategy that will use this credit card company's offer to the advantage of the restaurant and minimize the cost of implementing the scheme. You have recently taken a managerial economics course and have some idea of how to proceed even though you do not have the ability to come up with a demand curve for the restaurant, you don't have measures of price elasticity of demand or other useful demand indicators and you are using accounting cost information rather than economic cost information to make your decision.

Thus, you have to maximize the benefits of this credit card scheme for the restaurant and, at the same time, minimize the costs of implementing it without endangering the survival of the restaurant. Since you do not have marginal revenue or marginal cost information, your job is to make this scheme as efficient as possible in order to minimize costs and make the best decision for the restaurant. You know that this scheme, which is going to be marketed by the credit card firm, will not increase your advertisement and marketing costs but could help you bring more customers to the business.

a. Will you limit or put a minimum count on each table? That is, will you allow a party of two to use the benefit or will you require a minimum number of people on the party in order to take advantage of the offer?
b. Will you allow more than one person in the party to use the credit card to get the benefit? That is, if there is a party of 4 on a table, will you allow two people to pay with the credit card in order to take the discount on the third and fourth party member?
c. Will you cap the number of people on each party?
d. Will you include food and beverages in the offer or only the food? (Hint: try to research which type of restaurant items are more profitable or generate more margin for the restaurant)
e. Will you limit the offer to regular priced items in the menu or also include daily specials?
f. Will you come up with a mathematical equation that you will use to explain your strategy? Think about how you will minimize the cost for the restaurant of implementing this scheme and try to come up with a mathematical equation to help explain your strategy.