Teddy J is a manufacturer of dish washing liquid . If his monthly demand function for 750mlsize is q = 4000 - 250p and his total cost function is C(q) = 500 + 0.2q. i) How many 750ml bottles of dish washing liquid should Teddy J produce per month if he wishes to maximize his profits.
Teddy J is a manufacturer of dish washing liquid . If his monthly demand function for 750mlsize is q = 4000 - 250p and his total cost function is C(q) = 500 + 0.2q. i) How many 750ml bottles of dish washing liquid should Teddy J produce per month if he wishes to maximize his profits.
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter2: Functions
Section2.4: Average Rate Of Change Of A Function
Problem 4.2E: bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.
Related questions
Topic Video
Question
1) Teddy J is a manufacturer of dish washing liquid . If his monthly demand function for 750mlsize is q = 4000 - 250p and his total cost function is C(q) = 500 + 0.2q.
i) How many 750ml bottles of dish washing liquid should Teddy J produce
per month if he wishes to maximize his profits.
2) A poll commissioned by a politician estimates that t days after he makes a statement denegrating women, the percentage of his constituency those who support him at the time he made the statement that still supports him is given by
S(t) = 75(t2 - 3t + 25) ÷ t2 + 3t + 25
(iii) What was his minimum support level?
(iv) Was the approval rate positive or negative on the date of the election?
Transcribed Image Text:Step 3
75(12-3+25)
243+25
Given :S
(+3425) (75(-325))-75(12-3425) (+3e25)
(1243425)
(12+3425)(150-225)-(750-23+1875)(2+3)
(434425)
4s0(22-25)
(1243+25)
Step 4
His support is at lowest level when S'(1) = 0 (minima) or
450(12-25)
= 0
(1243++25)
= 450 (1 - 25) = 0
= ? - 25 = 0
>1 = 5,-5
As day should be positive,
=1 = 5 days.
For minimum support level check S"(5) > 0
2 (75(?-3423)
() = #0
*()-
1243+25
900(-'+75++75)
(12434+25)
S"
%3!
900(-sy+75x5+75)
I80
S"
(s7+3x5+25)
169
So, 1 = 5 will give lowest support.
Question 2 reference (Politician question)
Transcribed Image Text:Step 2
Obtain the profit function as follows:
a (q) = R (q) – C (q)
= 16q - - (500 + 0. 2q)
+ 15. 8q – 500
230
When q = 500, the profit function is,
1 (500) =
+ 15.8 (500) – 500
250
= 6400
Step 3
First derivative of profit function must be equated to zero; obtain the maximum profit.
x' (q) = (-+ 15. 8q – 500)
4+3950g-125000
%3D
250
= (-29 + 3950)
Put x' (q) = 0.
x' (q) = 0
(-29 + 3950) = 0
- 29 + 3950 = 0
q = 1975
When q = 1975, the profit is,
* (1975) = - 1975y
= 15102. 5
+ 15. 8 (1975) – 500
250
At q=500, profit is 6400 which is decreasing as maximum profit is 15102.5.
Question 1 reference (Teddy J)
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.Recommended textbooks for you
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning