A manufacturer produces bolts of a fabric with a fixed width. The quantity q 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 g = f(p). Then the total revenue earned with selling price p is R(p) = pf(p). (a) What does it mean to say that f(30) = 10,000? O There are 10,000 total yards of fabric and $275 to spend on it. O When the price of fabric is $30/yard, 10,000 yards will be sold. O When the price of fabric is $30/yard, 275 yards will be sold. O When the price of fabric is $275/yard, 30 yards will be sold. O There are 275 total yards of fabric and $30 to spend on it. What does it mean to say that f '(30) = -275? O As the price of the fabric decreases past $275/yard, the amount of fabric which will be sold is decreasing at a rate of $10,000 per (dollar per yard). O As the price of the fabric increases past $275/yard, the amount of fabric which will be sold is increasing at a rate of 30 yards per (dollar per yard). O As the price of the fabric decreases past $30/yard, the amount of fabric which will be sold is increasing at a rate of 10,000 yards per (dollar per yard). O As the price of the fabric decreases past $30/yard, the amount of fabric which will be sold is increasing at a rate of $275 per (dollar per yard). O As the price of the fabric increases past $30/yard, the amount of fabric which will be sold is decreasing at a rate of 275 yards per (dollar per yard). (b) Assuming the values in part (a), find R'(30). R'(30) = Interpret your answer. O As the price of fabric increases past $30/yard, the total revenue is increasing at $1750 per (dollar per yard). O As the price of fabric decreases past $30/yard, the total revenue is decreasing at $10,000 per (dollar per yard). O As the price of fabric decreases past $275/yard, the total revenue is increasing at $1750 per (dollar per yard). O As the price of fabric increases past $30/yard, the total revenue is decreasing at $275 per (dollar per yard). O As the price of fabric increases past $275/yard, the total revenue is increasing at $10,000 per (dollar per yard).