The total cost to produce 100 units of a certain commodity in a certain firm amounts to € 2800. Producing 500 units leads to a production cost of € 6000. Assume that the total production cost c (in €) is a linear function of the number q of units produced. a. Give the equation of the production cost function. The inverse demand function is given by p = 1000 - 1.25q, where p denotes the price of one unit of the product. b. Find the demand function. c. Express the total production cost c in terms of the price p.

The total cost to produce 100 units of a certain commodity in a certain firm amounts to € 2800. Producing 500 units leads to a production cost of € 6000. Assume that the total production cost c (in €) is a linear function of the number q of units produced. a. Give the equation of the production cost function. The inverse demand function is given by p = 1000 - 1.25q, where p denotes the price of one unit of the product. b. Find the demand function. c. Express the total production cost c in terms of the price p.

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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Question

7. The total cost to produce 100 units of a certain commodity in a certain firm amounts to € 2800.
Producing 500 units leads to a production cost of € 6000. Assume that the total production cost c
(in €) is a linear function of the number q of units produced.
a. Give the equation of the production cost function.
The inverse demand function is given by p = 1000 - 1.25q, where p denotes the price of one unit of the
product.
b. Find the demand function.
c. Express the total production cost c in terms of the price p.
Let P denote the profit (in €).
d. Show that the profit P is given by P = −1.25q² +992q - 2000.
e. Find the production levels for which the firm makes a profit between € 50 000 and € 150 000.
Round your answer to two decimals.

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