Ask Question, Ask an Expert

+1-415-315-9853

info@mywordsolution.com

Ask Math Expert


Home >> Math

M is not equal to m

P is not equal to p

Task (1)

The following four 4 equations are needed to be plotted as CONTOUR lines on the axes space (C, T) where C is the horizontal axis, and T is the vertical axis.
Contour lines for each equation should be between 6 and 8.

In total there should be five (5) plots, one for each equation, and the fifth which, is the most important, a plot with all the four equations are imposed on the same axes system (C, T)

M = (C) * ( 2*T + 0.028)                    (eq. 1)
P1 = (0.1237) * (C^(-4/3)) * (T) * ((T+1)^(1/3))        (eq. 2)
P2 = (0.003) * (C) * (T+1)                    (eq. 3)
P3 = 4 * (C^2) * (T) * (T+1)                    (eq 4)

M contour lines to be dashed lines, while P1, P2 and P3 to be solid lines in different colours.

No area filling, and no labeling are required.

Task (2)

Find the boundary between each two of the equations P1, P2, P3 by solving:

P1 = P2  ,  P1 = P3  ,  P2 = P3

Plot the boundary lines on a single figure that also includes the contours of M, P1, P2 and P3.

Task (3) 

Solve the optimality condition for each P equation against M according to the following relation:

Condition for Optimality:     ∇M = λ ∇P     with respect to C and T.

Note that the ∇is the gradient vector, and λ  is a scalar (the Langrange multiplier) so that:

M is the objective function and P is the constraint function.

The solution is obtained by differentiating M and P twice ( that is one time with respect to each variable C and T.

Then finding the values of  λ. And finally substituting in the constraint function P and find the values for C and T. (( In this method we assume that  ∇P  is NOT equal to zero.))

Thus, solve for C and T:

dM/dC  = λ  (dP/dC)      and     dM/dT  = λ  (dP/dT)

M will be the objective function, and P will be the constraint function.

Note  The total solution must be repeated three times:

∇M = λ ∇P1
∇M = λ ∇P2
∇M = λ ∇P3

Math, Academics

  • Category:- Math
  • Reference No.:- M91914

Have any Question? 


Related Questions in Math

Analyzenbspit collaboration technology and ecommerce

Analyze  IT collaboration technology and eCommerce techniques that can be applied to your project based on this week's readings ( Essentials of MIS , Chs. 9 and 10, and Week 3 Electronic Reserve Readings).  Create  a Mic ...

In the exercise prove the given theoremtheorem a set e sube

In the exercise prove the given theorem: Theorem A set E ⊆ R 2  is the set of Nash equilibrium payoffs in a two-player game in strategic form if and only if E is the union of a finite number of rectangles of the form [a, ...

Mathematical models are used as tools to describe reality

Mathematical models are used as tools to describe reality. These models are supposed to characterize the important features of the analyzed phenomena and provide insight. The normal distribution is an example of a random ...

1 draw the graph of the following linear function and give

1. Draw the graph of the following linear function and give the domain and range. f(x) = -½x + 5 2. Solve the following equation. |x| = 3. 3. Give the inequality whose graph is shown below. 4. Evaluate the following expr ...

What is meant by the end behavior of a polynomial function

What is meant by the end behavior of a polynomial function? Explain how to use the leading coefficient to determine the end behavior of the graph of a polynomial functions. Clarify the different cases and provide an exam ...

Innbsp300 words answer the following discussion post

In 300 words, answer the following discussion post question: The Green Organization is a conglomerate of many smaller business units. The organization has offices globally. Some offices are contracted independent agents ...

In which quadrant would the terminal side of theta lie and

In which, quadrant would the terminal side of θ lie and is subject to the given conditions cos θ 0?

A store has clearance items that have been marked down by

A store has clearance items that have been marked down by 50%. They are having a sale, advertising an additional 35% off clearance items. What percent of the original price do you end up paying?

The set of equilibria is a subset of the product

The set of equilibria is a subset of the product space Δ(S 1 ) × Δ(S 2 ) × ... × Δ(S n ). Prove that it is a compact set. Is it also a convex set? If you answer yes, provide a proof; if you answer no, provide a counterex ...

Explain how the florida foreclosure process is similar to

Explain how the Florida Foreclosure process is similar to the Florida residential Landlord Tenant Eviction Process. Explain the rationale/public policy behind these processes. Is Florida a Lien Theory State or a Title Th ...

  • 4,153,160 Questions Asked
  • 13,132 Experts
  • 2,558,936 Questions Answered

Ask Experts for help!!

Looking for Assignment Help?

Start excelling in your Courses, Get help with Assignment

Write us your full requirement for evaluation and you will receive response within 20 minutes turnaround time.

Ask Now Help with Problems, Get a Best Answer

WalMart Identification of theory and critical discussion

Drawing on the prescribed text and/or relevant academic literature, produce a paper which discusses the nature of group

Section onea in an atwood machine suppose two objects of

SECTION ONE (a) In an Atwood Machine, suppose two objects of unequal mass are hung vertically over a frictionless

Part 1you work in hr for a company that operates a factory

Part 1: You work in HR for a company that operates a factory manufacturing fiberglass. There are several hundred empl

Details on advanced accounting paperthis paper is intended

DETAILS ON ADVANCED ACCOUNTING PAPER This paper is intended for students to apply the theoretical knowledge around ac

Create a provider database and related reports and queries

Create a provider database and related reports and queries to capture contact information for potential PC component pro