A market survey shows that for every $ 0.10 reduction in the price, 40 more sandwiches will be sold. How much should the deli charge in order to maximize revenue?

$2.40

Explanation:

Here is the complete question: A deli sells 320 sandwiches per day at a price of $4 each.

A market survey shows that for every $ 0.10 reduction in the price, 40 more sandwiches will be sold. How much should the deli charge in order to maximize revenue?

Given: Number of sandwiches sold per day is 320.

           Price of each sandwich is $4.

           For every $0.10 reduction in the price, 40 more sandwiches will be sold.

Let´s assume price of each sandwich sold at new reduced price be "x" times.

∴ New price of sandwich is

As given, for every $ 0.10 reduction in the price, 40 more sandwiches will be sold.

∴ Total number of sandwiches sold at new price=

We know, revenue=

⇒ revenue=

using distributive property of multiplication.

⇒ revenue=

Considering the revenue to be R(x)

Now taking derivatives of the revenue.

=

Solving it.

We get,

Finding critical points by setting derivative equal to 0

R´(x)⇒

Subtracting both side by 128

⇒

Dividing both side by -8

⇒

∴ x= 16

Hence, price of each sandwich is reduced by $0.10 is 16 times.

Next, finding cost of each sandwich to maximize revenue.

cost of each sandwich to maximize revenue=

∴ Cost of each sandwich to maximize revenue=

Hence, Deli should charges $2.40 for each sandwich to maximize revenue.

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