Chapter 14.4, Problem 32E

The manager of the Sea Islands Chicken Shack is interested in finding new ways to improve sales and profitability. Currently, Sea Islands offers both “eat-in” and “take-out" chicken dinners at $3.25 each, sells 6250 dinners per week, and has short-run weekly costs (in dollars) given by

$C=500+1.2x$

where $x$ is the total number of eat-in and take-out chicken dinners.

The Sea Islands manager recently commissioned a local consulting firm to study the eat-in and take-out market demand per week. The study results provided the following weekly demand estimates for each of the two market segments:

Eat-in: $x=6000—1000p_x$ Take out: $y=10,000-2000p_y$

where $x$ is the number of eat-in dinners, with $p_x$ as the price of each, and y is the number of take-out dinners, with $p_y$ as the price of each. Use this information in Problems 31 and 32.

When eat-in and take-out dinners are considered separately, Sea Islands Chicken Shack’s short-run weekly cost function becomes

$C=500+0.60x+1.60y$

(a) Use this revised cost function to find the number of eat-in and take-out chicken dinners that would give maximum profit.

(b) What price should be charged for each type of dinner now, and what is the maximum weekly profit?

(c) Based on the results of parts (a) and (b), which is the best pricing strategy? Explain.