commodity has a demand function modeled by p = 128 0.5x and a total cost function modeled by C = 50x + 35.75, where x is the number of units. a) What unit price (in dollars) yields a maximum profit? per unit ) When the profit is maximized, what is the average cost (in dollars) per unit? (Round your answer to two decimal places.) per unit

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Problem:**

A commodity has a demand function modeled by \( p = 128 - 0.5x \) and a total cost function modeled by \( C = 50x + 35.75 \), where \( x \) is the number of units.

(a) What unit price (in dollars) yields a maximum profit?

$ \_\_\_\_\_\_\_\_ \text{ per unit}

(b) When the profit is maximized, what is the average cost (in dollars) per unit? (Round your answer to two decimal places.)

$ \_\_\_\_\_\_\_\_ \text{ per unit}
Transcribed Image Text:**Problem:** A commodity has a demand function modeled by \( p = 128 - 0.5x \) and a total cost function modeled by \( C = 50x + 35.75 \), where \( x \) is the number of units. (a) What unit price (in dollars) yields a maximum profit? $ \_\_\_\_\_\_\_\_ \text{ per unit} (b) When the profit is maximized, what is the average cost (in dollars) per unit? (Round your answer to two decimal places.) $ \_\_\_\_\_\_\_\_ \text{ per unit}
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