Vincenzo Pizzeria Limited operates the only pizza place in town although there are several other fast-food outlets in peripheral competition with Vincenzo. The manager, Vincenzo Fiorelli, feels that he has a virtual monopoly, since his clientele is largely comprised of fervent pizza lovers, and that selling more pizzas is just a matter of inducing people to “eat out” more often. Consequently Mr. Fiorelli holds prices constant and advertises in local newspapers and on a local television. His pizzas come in three sizes and with a variety of toppings, from “plain (to¬ mato paste and cheese) all the way up to “deluxe” (mushrooms, peppers, olives, ground beef, pepperoni, and heaps of mozzarella cheese).

Mr. Firorelli’s son Paolo has recently obtained his business degree and has joined the family business as marketing manager. Paolo is interested in maximizing profits of the enter¬ prise, since his father has promised him half of any extra profits generated as a bonus. Paolo decides to conduct an analysis of the cost and demand conditions facing the firm. First he exam¬ ines the cost structure. Given the three different sizes of pizza and the various combinations of toppings, the firm is in effect offering a very broad product line. Paolo’s first task is to convert all the product offerings into the terms of a common denominator, which he calls a medium- pizza equivalent (MPE). The weights attached to each product reflect the relative variable costs of that product. Thus a medium-deluxe pizza is equal to 1 MPE, a small-deluxe pizza is equal to 0.75 MPE and a large-deluxe is equal to 1.5 MPEs, with lower weights given in each size category where the pizza is less than deluxe. The average variable cost of an MPE is $2.65, and Paolo finds this to be constant in the relevant output range. The first major decision Paolo makes is to standardize prices on all pizzas by marking up the average variable cost by 50 per¬ cent.

The marketing manager then undertakes a study of demand conditions. After examining past records and interviewing a random sample of five hundred customers and potential cus¬ tomers, Paolo generates the following demand function for Vincenzo’s pizzas:

Q = 28105.1 - 5842.2P + 1061.6/4 - 22.5A2 where Q is the number of MPEs demanded per month; P is the price of an MPE in dollars; and A is the advertising and promotional expenditures per month in thousands of dollars.

At present, prices are as indicated by the above markup-pricing policy, and advertising and promotional expenditures are running at the rate of $8,000 per month.

(a) Using graphical analysis (with algebraic confirmation of results), find the optimal price and advertising/promotional levels.