Chapter 10, Problem 43RE

### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

Chapter
Section

### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Profit The monthly demand function for x units of a product sold at $p per unit by a monopoly is p = 800 — x , and its average cost is C ¯ = 200 + x .(a) Determine the quantity that will maximize profit.(b) Find the selling price at the optimal quantity. (a) To determine To calculate: The quantity that will maximize the profit if the function for x units for the monthly demand of a product is p=800x, sold at$p per unit by a monopoly and the average cost is C¯=200+x.

Explanation

Given Information:

The provided equations are the monthly demand function for x units of a product sold at $p per unit by a monopoly is p=800x and the average cost is C¯=200+x. Formula Used: P(x)=R(x)C(x) Where R(x)andC(x) are total revenue function and total cost function. Calculation: Consider the provided equation C¯=200+x, for x units of a product sold, The revenue for p=800x is, Revenue=(800x)x=800xx2 The cost is: C¯=200+xC=(200+x)x=200x+x2 Hence, the profit function is equal to: P=RC=800xx2200xx2= (b) To determine To calculate: The selling price at optimal quantity if the function for x units for the monthly demand of a product is p=800x, sold at$p per unit by a monopoly and the average cost is C¯=200+x.

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