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(i) The price p, in dollars, of a certain commodity and the quantity x sold obey the demandequation p = −15x + 200 where 0 ≤ x ≤ 1000Suppose that the cost C, in dollars, of producing x units is C =√x10 + 400Assuming that all items produced are sold, find the cost C as a function of the price p.(ii)The profit function,in dollars, for a product is given byΠ(x) = −x3 + 76x2 − 380x − 2800,where x is the number of units produced and sold.If break-even occurs when 10 units areproduced and sold,(a) Find a quadratic factor of Π(x).(b) Find a number of units other than 10 that gives break-even for the product.

(i) The price p, in dollars, of a certain commodity and the quantity x sold obey the demandequation p = −15x + 200 where 0 ≤ x ≤ 1000Suppose that the cost C, in dollars, of producing x units is C =√x10 + 400Assuming that all items produced are sold, find the cost C as a function of the price p.(ii)The profit function,in dollars, for a product is given byΠ(x) = −x3 + 76x2 − 380x − 2800,where x is the number of units produced and sold.If break-even occurs when 10 units areproduced and sold,(a) Find a quadratic factor of Π(x).(b) Find a number of units other than 10 that gives break-even for the product.

College Algebra
College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Rational Functions And Conics
Section4.2: Graphs Of Rational Functions
Problem 88E
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(i) The price p, in dollars, of a certain commodity and the quantity x sold obey the demand
equation p = −
1
5
x + 200 where 0 ≤ x ≤ 1000
Suppose that the cost C, in dollars, of producing x units is C =
√x
10 + 400
Assuming that all items produced are sold, find the cost C as a function of the price p.
(ii)
The profit function,in dollars, for a product is given by
Π(x) = −x
3 + 76x
2 − 380x − 2800,
where x is the number of units produced and sold.If break-even occurs when 10 units are
produced and sold,
(a) Find a quadratic factor of Π(x).
(b) Find a number of units other than 10 that gives break-even for the product.

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