Answer :
Answer:
(a) q = -360p +29440
(b) maximum revenue of $601,884 at p = 40.89
Step-by-step explanation:
(a) Demand Equation
You are given to pairs of p and q:
(p, q) = (54, 10000) and (79, 1000)
These can be used in the 2-point form of the equation for a line:
q = (q2 -q1)/(p2 -p1)(p -p1) +q1
q = (1000 -10000)/(79 -54)(p -54) +10000 . . . . . substitute givens
q = (-9000/25)(p -54) +10000 . . . . . . . . . . . . . . . simplify a bit
q = -360p +29440 . . . . . . . . . . . . . . . . . . . . . . . . . write in slope-intercept form
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(b) Maximum Revenue
Revenue from book sales will be the product of the quantity sold (q) and the price at which they are sold (p). Here, that means ...
r(p) = p·q = p(-360p +29440) = 360p(81 7/9 -p)
This is the equation of a parabola that opens downward. Its axis of symmetry is at the price point halfway between the zeros of p=0 and p=81.78. That is, the revenue will be maximized at a unit price of 40.89. That maximum revenue will be about ...
r(40.89) ≈ $601,884.44
Big Book Publishing's annual revenue is predicted to be about $601,884 at a book price of $40.89.
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Comment on the numbers
Both the price and the revenue are repeating decimal fractions if these equations are taken at face value. If quantity is rounded to whole books and price is rounded to cents, then the maximum revenue is predicted to be $601,900.80 on sales of 14,720 books at a price of $40.89 each.
