Consider the following price demand function p(x)= 93– 2x and the cost function C(x)= 340+19x. Here x is in thousands of items, and p(x) is in S. Thecorresponding Revenue and Profit functions are R(x) = 93x – 2x and P(r)= 74x - 2x²- 340. How many items need to be sold in order to maximize theREVENUE function?Oa. 23.25 thousand itemsO b. 344.50 thousand itemsO C. 56.00 thousand itemsOd. 18.50 thousand itemse. 5.38 thousand items

Answered: Consider the following price demand…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Consider the following price demand function p(x)= 93– 2x and the cost function C(x)= 340+19x. Here x is in thousands of items, and p(x) is in S. The
corresponding Revenue and Profit functions are R(x) = 93x – 2x and P(r)= 74x - 2x²- 340. How many items need to be sold in order to maximize the
REVENUE function?
Oa. 23.25 thousand items
O b. 344.50 thousand items
O C. 56.00 thousand items
Od. 18.50 thousand items
e. 5.38 thousand items

Expert Solution

Step 1

It is given that the revenue function is $R (x) = 93 x - 2 x^{2}$ .

To maximize the revenue function, firstly the critical points has to be found out and it has to be checked that the second derivative is less than 0 at this point.

Obtain the critical points by equating the derivative of $R (x) = 93 x - 2 x^{2}$ to 0:

$R' (x) = 0 93 - 4 x = 0 93 = 4 x x = 23.25$

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