A deli sells 480 sandwiches per day at a price of $4 each. A market survey shows

Question

A deli sells 480 sandwiches per day at a price of $4 each. A market survey shows that for every $0.10 reduction in the price, 20 more sandwiches will be sold. How much should the deli charge in order to maximize revenue? The deli should charge 3.20 for a sandwich to maximize revenue. (Round to the nearest cent as needed.) A different market survey should that for every $0.20 reduction in the original $4 price, 5 more sandwiches will be sold. Now how much should the deli charge in order to maximize revenue? Now the deli should charge $ for a sandwich to maximize revenue. (Round to the nearest cent as needed.)

Explanation / Answer

( 480 + 20x ) ( 4 - 0.1x )

to maximize the derivative is 0

hence 80 - 2x - 48 - 2x = 0

x = 8

so he will sell 640 sandwiches at $3.2

b)

( 480 + 5x ) * ( 4 - 0.2x )

20 - x -96 -x

x = -38

if possible he has to sell 290 sandwhiches at $11.6, if a $0.2 increase in price results in reduction in demand by 5.

If not just stick to the current price of $4 for 480 sandwiches

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