Record Breakers is a downtown store selling phonograph records and tapes. Its nearest compet¬ itor is about six blocks away, and its clientele is composed almost entirely of downtown office workers and other personnel from nearby buildings. Record Breakers has found that the sales of phonograph records vary with the number of records it places on special at $3.99 (compared with the regular price of $6.99) and with the space purchased in the city’s morning newspaper for advertising these specials. The specials are intended to attract customers into the store where they will (it is hoped) also purchase one or more other records at the regular price. The greater the number of specials offered, the lower the total revenue per record, or average price of the records sold. Given any specific number of records on special, the store finds that record sales vary positively, but with diminishing returns, with the area devoted to advertising these particular records in the newspaper. Regression analysis indicates that Q = 624.3 - 216.52P + 481.85 - 35.85A2 where Q represents the weekly sales (units) of albums; P is average price in dollars; and S is space units (100 square inches daily for five days) in the morning newspaper. This regression equation is highly significant and explains virtually all the variation in weekly record sales.

The average variable cost per record is constant at $3 and space units in the newspaper cost $300, and this space is available in continuously variable fractions of a unit. The “average” situation is that Record Breakers will place six records on special and buy 2.5 units of advertis¬ ing space each week. This combination causes the average price to be $5.75 over all records sold. The relationship between average price and number of records on special has been esti¬ mated as Av.P = 6.93 — 0.19 NS (with R2 = 0.97, significant at the 5 percent level) over the range of one to fifteen records on special. This relationship holds independently of the units of advertising space purchased, although the latter does influence volume, as indicated by the earlier regression equation.

(a) Using graphical analysis, find the level of average price and the level of advertising space purchased that allow short-run profit contribution to be maximized.

(b) How many records should be put on special each week? Explain.