logo

Marginal Functions in Economics

8 Pages812 Words49 Views
   

Added on  2021-04-22

Marginal Functions in Economics

   Added on 2021-04-22

ShareRelated Documents
MONTGOMERY COUNTY COMMUNITY COLLEGEMAT 142Exam 2Walter R. HunterName _______________________________ 1.Given the graph of the Marginal Profit function, explain what points A and B implyabout the profit function.SolutionPoint A: The point where the marginal profit is maximum and this is equal to 10Point B: Point where the marginal profit is equal to zero 2.Given the graph of P(x), locate the point of diminishing returns.0100200300400500600012345The point of diminishing returns is at 4mat\wh\mat142\sp03\t21015-510ABMP
Marginal Functions in Economics_1
3.Suppose that the total number of units produced by a worker in t hours of an 8 hour daycan be modeled byP(t) = 25t + 6t2 t3Find the point of diminishing returns. Explain what this point means in terms of unitsproduced by a worker.SolutionP(t)=25t+6t2t3dPdt=25+12t−3t2Solving25+12t−3t2 yieldst=5.51∧−1.51But we can’t have negative time. Next we check whether it is aminimum or a maximumd2Pdt2=12−6t<0,t=5.51ismaximumThus Diminished returnt=5.51Maximum units = 25(5.51)+6(5.51)2(5.51)3=152.63≈153This point means that for maximum units to be produced a worker has to work for 5.51 hours and the maximum units at this time is 153 units. 4.The weekly sales S of a product during an advertising campaign are given by226tStt25, 0 t 20a.Use calculus to find the critical values that lie in the domain of the problem.Solutionmat\wh\mat142\sp03\t22
Marginal Functions in Economics_2
To find the critical values then we have to find the derivative of S(t)S'(t)=(t2+25)ddt(26t)−26tddt(t2+25)(t2+25)2¿(t2+25)26−26t(2t)(t2+25)2¿650−26t2(t2+25)2To get critical valuesS'(t)=0. Thus650−26t2(t2+25)2=0650=26t2t2=65026=25t=5The graph is given below;b.Over what interval in the domain do the sales decrease?SolutionThe sales decrease in the time interval of [5, 20]mat\wh\mat142\sp03\t23
Marginal Functions in Economics_3

End of preview

Want to access all the pages? Upload your documents or become a member.

Related Documents
MATH 142 Calculus for Business
|8
|514
|119

Optimizing Costs and Profits for Desklib: A Study
|4
|711
|161

Assignment On Math 107 Problems
|9
|683
|18

Algebra - Desklib
|8
|693
|479

Solved Assignments and Study Material for Desklib
|6
|1037
|48

Real-World Applications
|20
|2735
|12