MaplePrimes Questions


 

In this code k=2 and Beta=2 has been cconsidered

Loading Optimization

Loading Student:-MultivariateCalculus

ISO ELASTIC DEM ADD ERROR

y := proc (p, e) options operator, arrow; alpha-beta*p+k*e end proc:

G := g(p):

NULL

g := proc (e) options operator, arrow; (1/2)*mu*e^2 end proc:

 

Lambda := proc (z) options operator, arrow; int((z-u)*phi(u), u = 0 .. z) end proc: 

``

``

NULL

Step 1  Integrated supply chain

THE EXPECTED total PROFIT FUNCTION w r t LINEAR DEMAND

 

PI := proc (p, e, z) options operator, arrow; (p-c)*(y(p, e)-z)-(p-v)*Lambda(z)-g(e) end proc

proc (p, e, z) options operator, arrow; (p-c)*(y(p, e)-z)-(p-v)*Lambda(z)-g(e) end proc

(1)

PI(p, e, z)

(p-c)*(-beta*p+e*k+alpha-z)-(p-v)*(int((z-u)*phi(u), u = 0 .. z))-(1/2)*mu*e^2

(2)

FIRST PUT ALL PARAMETER VALUES AND THEN GO FOR THE DIFFERENTIATION

RUN THE OPTIMALITY AND THE SUBROUTINES FOR DIFFERENT Beta and K values

CASE 1:   Put k = 2 and beta =2

beta

(3)

`` 
Int_Profit := simplify(eval(PI(p, e, z), [k = 2, beta = 2, alpha = 50, mu = 10, c = 5, v = 1, phi(u) = 1/2]))

-2*p^2+(1/4)*(-z^2+8*e-4*z+240)*p-5*e^2+(1/4)*z^2-10*e+5*z-250

(4)

Int_Profit[1][1]

(-2*p^2+(1/4)*(-z^2+8*e-4*z+240)*p-5*e^2+(1/4)*z^2-10*e+5*z-250)[1][1]

(5)

 

Optimization:-NLPSolve(Int_Profit, p = 0 .. 60, e = -1000 .. 30, z = -10000 .. 25, initialpoint = {e = 0, p = 10, z = 0}, maximize)

[230.512568949745969, [e = HFloat(2.274015113534025), p = HFloat(16.370075567375324), z = HFloat(-1.4795080892429795)]]

(6)

NULL

Int_Profit

-2*p^2+(1/4)*(-z^2+8*e-4*z+240)*p-5*e^2+(1/4)*z^2-10*e+5*z-250

(7)

Calculate the Value of q

``

q := z+y(p, e)

-beta*p+e*k+alpha+z

(8)

qopt := simplify(eval(q, [e = 2.27401511353403, p = 16.3700755673753, z = 1.47950808924298, k = 2, beta = 2, alpha = 50, mu = 10, c = 5, v = 1, phi(u) = 1/2]))

23.28738718

(9)

Step 2  Decentralized supply chain

Retailer's profit

 

`#msubsup(mi("Π",fontstyle = "normal"),mi("R"),mi("d"))` := proc (p, e, q, w) options operator, arrow; (p-w)*(y(p, e)-z)-(p-v)*Lambda(z)-g(e) end proc

proc (p, e, q, w) options operator, arrow; (p-w)*(y(p, e)-z)-(p-v)*Lambda(z)-g(e) end proc

(10)

Re_Profit := simplify(eval(`#msubsup(mi("Π",fontstyle = "normal"),mi("R"),mi("d"))`(p, e, q, w), [alpha = 50, beta = 2, k = 2, mu = 10, c = 5, v = 1, phi(u) = 1/2, w = 10]))

-2*p^2+(1/4)*(-z^2+8*e-4*z+280)*p-5*e^2+(1/4)*z^2-20*e+10*z-500

(11)

Optimization:-NLPSolve(Re_Profit, p = 0 .. 60, e = -1000 .. 30, z = -10000 .. 25, initialpoint = {e = 0, p = 10, z = 0}, maximize)

[129.081143396165999, [e = HFloat(1.7075918734530873), p = HFloat(18.537959441958364), z = HFloat(-0.9736548233351249)]]

(12)

 

``

``

Optimal q value for decentralized supply chain

 

qd_opt := simplify(eval(q, [e = 1.70759187345309, p = 18.5379594419584, z = .973654823335125, k = 2, beta = 2, alpha = 50, mu = 10, c = 5, v = 1, phi(u) = 1/2]))

17.31291969

(13)

Manufacture's Profit

 

`#msubsup(mi("Π",fontstyle = "normal"),mi("M"),mi("d"))` := proc (p, e, q) options operator, arrow; (w-c)*qd_opt end proc

proc (p, e, q) options operator, arrow; (w-c)*qd_opt end proc

(14)

M_Profit := simplify(eval(`#msubsup(mi("Π",fontstyle = "normal"),mi("M"),mi("d"))`(p, e, q), [qd_opt = 17.31291969, alpha = 50, beta = 2, k = 2, mu = 10, c = 5, v = 1, phi(u) = 1/2, w = 10]))

86.56459845

(15)

Total Wholesale Profit

`#msup(mi("Π",fontstyle = "normal"),mi("d"))` := proc (p, e, q) options operator, arrow; M_Profit+R_Profit end proc

proc (p, e, q) options operator, arrow; M_Profit+R_Profit end proc

(16)

Whole_Profit := eval(`#msup(mi("Π",fontstyle = "normal"),mi("d"))`(p, e, q), [M_Profit = 86.56459845, R_Profit = 129.08114339616599])

215.6457418

(17)

step 3 find the t value

t := (In_Profit-R_Profit)/(w-c)

(In_Profit-R_Profit)/(w-c)

(18)

 

topt := eval(t, [w = 10, c = 5, In_Profit = 230.512568949745969, R_Profit = 129.08114339616599])

20.28628510

(19)

 

Hence range of t is 17.31 to 20.28

 

 

 


 

Download Code_1.mw

I have
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Do others have problem installing this?  I'll try again in few hrs, it might be the Maple server is having some issues but thought to ask.

 

 

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given is the lower, partial differential equation. I have solved this (hopefully) correctly. I was given the tip to do in Maple a simple control in which the solution is inserted into the original equation. Since I'm quite inexperienced in maple, I would like to ask you for help on how I do that best!

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Hi, I'm trying to plot the following functions in 3 dimensions using the following:

plot3d(kappa*sech(kappa*(-k^2*t+x)), x = -10 .. 10, t = -10 .. 10)

plot3d((2*(-K^2+k^2))*(K*cosh(k*(-k^2*t+x))+k*cosh(K*(-K^2*t+x)))/((K+k)^2*cosh(k*(-k^2*t+x)-K*(-K^2*t+x))+(-K+k)^2*cosh(k*(-k^2*t+x)+K*(-K^2*t+x))+4*K*k), x = -10 .. 10, t = -10 .. 10)

plot3d(2*(diff(arctan(lambda*sin(mu*((-3*lambda^2+mu^2)*t+x))*sech(lambda*((-lambda^2+3*mu^2)*t+x))/mu), x)), x = -10 .. 10, t = -10 .. 10);

Each produces an empty plot with a message similar to the following:
Warning, expecting only range variables [x, t] in expression 2*(lambda*cos(mu*((-3*lambda^2+mu^2)*t+x))*sech(lambda*((-lambda^2+3*mu^2)*t+x))-lambda^2/mu*sin(mu*((-3*lambda^2+mu^2)*t+x))*sech(lambda*((-lambda^2+3*mu^2)*t+x))*tanh(lambda*((-lambda^2+3*mu^2)*t+x)))/(lambda^2/mu^2*sin(mu*((-3*lambda^2+mu^2)*t+x))^2*sech(lambda*((-lambda^2+3*mu^2)*t+x))^2+1) to be plotted but found names [lambda, mu]

in each case kappa, k, K, lambda, mu are real constants 

 

Thanks for any help with this
 

 

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===

===

 

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Suppose we have a set of quadratic equations of the form:

 

U_11 * a * q + U_12 * b * q + U_13 * c * q + U_14 * d * q + U_15 * a * w + U_16 * b * w + U_17 * c * w + U_18 * d * w + .. = C_i

.

.

.

 

Where terms in uppercase means constant while lowercase letters correspond to unknowns.

 

Now, I want to make a change of variable, so instead of having non-linear term `a * q` we would have `s_ij`, meaning i-th equation and j-th unknown after the change was done.

 

I'm trying to do so, because in my case I will be left with a linear system with a small number of unknowns(relative to N) and N equations, and so I could then solve it easily.

 

Any help is appreciated, thank you!

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