**Question 9: Profit Maximization for Tire Manufacturing**A manufacturer can produce tires at a cost of $20 each. It is estimated that if the tires are sold for $ p $ dollars each, consumers will buy $ 1560 - 12p $ of them each month. - **Task:** - Express the manufacturer's monthly profit as a function of price. - Graph the function. - Use the graph to determine the optimal selling price. - Determine how many tires will be sold each month at the optimal price.**Explanation:**To solve this problem, use the following steps:1. **Determine the Profit Function:** - Revenue from selling tires is given by $ R = p \times (1560 - 12p) $. - Cost of producing these tires is given by $ C = 20 \times (1560 - 12p) $. - Profit $ \pi $ is calculated as $ \pi = R - C $.2. **Graph the Profit Function:** - Plot a graph with price ($ p $) on the x-axis and profit on the y-axis based on the derived profit function. - Identify the vertex of the parabola, which represents the maximum profit.3. **Find the Optimal Price:** - The optimal price is the value of $ p $ at which the profit function reaches its maximum.4. **Calculate Tires Sold at Optimal Price:** - Substitute the optimal price back into the demand function $ 1560 - 12p $ to find the number of tires sold.This exercise involves applying concepts of quadratic functions and graph analysis to determine optimal pricing strategies in a business context.

Given information Cost of producing each tire =$20 Tires are sold for p dollars for a piece Number…

9. A manufacturer can produce tires at a cost of $20 apiece. It is estimated that is the tires are sold for p dollars apiece, consumers will buy 1,560 – 12p of them each month. Express the manufacturer's monthly profit as a function of price, graph the function, and use the graph to determine the optimal selling price. How many tires will be sold each month at the optimal price?

9. A manufacturer can produce tires at a cost of $20 apiece. It is estimated that is the tires are sold for p dollars apiece, consumers will buy 1,560 – 12p of them each month. Express the manufacturer's monthly profit as a function of price, graph the function, and use the graph to determine the optimal selling price. How many tires will be sold each month at the optimal price?

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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