What price should be charged for each type of dinner

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Reference no: EM131801584

Question: 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_yas the price of each.

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?

Reference no: EM131801584

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