Solve the Problem
-The Daily Profit in Dollars of a Specialty

question 64

Multiple Choice

Solve the problem
-The daily profit in dollars of a specialty cake shop is described by the function $P ( x ) = - 4 x ^ { 2 } + 208 x - 1920$ , where $x$ is the number of cakes prepared in one day. The maximum profit for the company occurs at the vertex of the parabola. How many cakes should be prepared per day in order to maximize profit?

• A) 2704 cakes
• B) 26 cakes
• C) \(676 \mathrm { cakes }\)
• D) \(52 \mathrm { cakes }\)

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Definitions:

Producer Surplus

The difference between what producers are willing to accept for a good versus what they actually receive, due to higher market price.

Individual Producer Surplus

The net gain to an individual seller from selling a good; equal to the difference between the price received and the seller’s cost.

Phantom Tickets

Tickets for an event that are sold or promised to a customer but actually do not exist or are not available.

Producer Surplus

Producer surplus refers to the difference between what producers are willing to accept for a good or service versus what they actually receive, essentially measuring the benefit or surplus producers gain from transactions.