A Manufacturer Produces Bolts Of A Fabric With A Fixed Width The Quantity Of This Fabric Measured In Yards That Is So 1 (130.36 KiB) Viewed 32 times
A manufacturer produces bolts of a fabric with a fixed width. The quantity of this fabric (measured in yards) that is sold is a function of the selling price p in dollars per yard), so we can write q = f(p). Then the total revenue earned with selling price p is R() = pf(p). (a) What does it mean to say that f(15) = 10,000? O When the price of fabric is $15/yard, 550 yards will be sold. There are 10,000 total yards of fabric and $550 to spend on it. There are 550 total yards of fabric and $15 to spend on it. O When the price of fabric is $15/yard, 10,000 yards will be sold. When the price of fabric is $550/yard, 15 yards will be sold. What does it mean to say that f'(15) = -550? O As the price of the fabric increases past $550/yard, the amount of fabric which will be sold is increasing at a rate of 15 yards per (dollar per yard). As the price of the fabric decreases past $15/yard, the amount of fabric which will be sold is increasing at a rate of $550 per dollar per yard). O As the price of the fabric decreases past $550/yard, the amount of fabric which will be sold is decreasing at a rate of $10,000 per (dollar per yard). As the price of the fabric decreases past $15/yard, the amount of fabric which will be sold is increasing at a rate of 10,000 yards per (dollar per yard). As the price of the fabric increases past $15/yard, the amount of fabric which will be sold is decreasing at a rate of 550 yards per (dollar per yard). (b) Assuming the values in part (a), find R'(15). R'(15) = Interpret your answer. O As the price of fabric decreases past $15/yard, the total revenue is decreasing at $10,000 per (dollar per yard). O As the price of fabric increases past $550/yard, the total revenue is increasing at $10,000 per (dollar per yard). As the price of fabric decreases past $550/yard, the total revenue is increasing at $1750 per (dollar per yard). O As the price of fabric increases past $15/yard, the total revenue is decreasing at $550 per dollar per yard). As the price of fabric increases past $15/yard, the total revenue is increasing at $1750 per (dollar per yard). Need Help? Read It Submit Answer
In this exercise, we estimate the rate at which the total personal income is rising in a metropolitan area. In 1999, the population of this area was 987,200, and the population was increasing at roughly 9500 people per year. The average annual income was $31,775 per capita, and this average was increasing at about $1300 per year (a little above the national average of about $1225 yearly). Use the Product Rule and these figures to estimate the rate at which total personal income was rising in the area in 1999. (Round your answer to three decimal places.) $ x billion per year Enhanced Feedback Please try again. For finding the rate of change of total personal income, start by finding a function for total personal income by multiplying together two other functions. Then, differentiate the function using the product rule and plug in the given values. ------------------------- Need Help? Read It Watch It
Join a community of subject matter experts. Register for FREE to view solutions, replies, and use search function. Request answer by replying!