A business has found that it can sell 680 items if it sets its price to $66.9. However, if it lowers its price to $40.19, it can sell 930 item: a) Find the linear demand equation (price function) for selling x items. (round to 4 decimal places) p (2) = It costs the business $5.62 per item to produce and they have $2,500 in overhead each month. (b) Find the linear Cost, and quadratic Revenue and Profit functions for producing/selling x items: (round to 4 decimal places) C (2) = Number x+ Number R(x) = Number 2+Number x+ Number P (x) = Number 2+ Number x+ Number

Microeconomic Theory
12th Edition
ISBN:9781337517942
Author:NICHOLSON
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Chapter11: Profit Maximization
Section: Chapter Questions
Problem 11.4P
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A business has found that it can sell 680 items if it sets its price to $66.9. However, if it lowers its price to $40.19, it can sell 930 items.
a) Find the linear demand equation (price function) for selling x items. (round to 4 decimal places)
p (2) =
It costs the business $5.62 per item to produce and they have $2,500 in overhead each month.
(b) Find the linear Cost, and quadratic Revenue and Profit functions for producing/selling x items: (round to 4 decimal places)
C (x) = Number
x+ Number
%3D
R(x) =
Number
x2+ Number
x+ Number
P (x) =
Number
x+Number
x+ Number
(c) How many items should the company sell to break even? What price should they set to do so?
(lower quantity) They could sell Number
items at a price of $ Number
each OR
(higher quantity) They could sell Number
items at a price of $ Number
each
Transcribed Image Text:A business has found that it can sell 680 items if it sets its price to $66.9. However, if it lowers its price to $40.19, it can sell 930 items. a) Find the linear demand equation (price function) for selling x items. (round to 4 decimal places) p (2) = It costs the business $5.62 per item to produce and they have $2,500 in overhead each month. (b) Find the linear Cost, and quadratic Revenue and Profit functions for producing/selling x items: (round to 4 decimal places) C (x) = Number x+ Number %3D R(x) = Number x2+ Number x+ Number P (x) = Number x+Number x+ Number (c) How many items should the company sell to break even? What price should they set to do so? (lower quantity) They could sell Number items at a price of $ Number each OR (higher quantity) They could sell Number items at a price of $ Number each
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