A large juice company wants to introduce some new flavor combinations involving cranberry juice, apple juice, and grape juice. To get started, samples of various mixtures of juice are prepared in 200 gallon vats.

John Rich and Brian RileyFirst suppose a 200 gallon vat starts out full of pure apple juice and pure cranberry juice is added at 5 gallons per minute while thoroughly mixed juice is removed at 5 gallons per minute.

Set up a model in Maple for the amount of cranberry juice in the vat as a function of time.restart:with(DEtools):with(plots):

Warning, the name changecoords has been redefined

diffeq:=diff(s(t),t)=((200-s(t))/40);

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Have Maple find all equilibrium solutions.s:='s';

NiM+SSJzRzYiRiQ=

diffeq;

NiMvLUklZGlmZkdJKnByb3RlY3RlZEdGJjYkLUkic0c2IjYjSSJ0R0YqRiwsJiIiJiIiIkYoIyEiIiIjUw==

soln:=dsolve(diffeq,s(t));

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A new flavor combination created using juice extracted from the vat after 20 minutes did very well on blind taste tests and the company wants to recreate the recipe. Use Maple to do Euler's method with 10 steps to estimate the amount of cranberry juice in the vat after 20 minutes.restart;withplots:DE(tools):de:= diff(s(t),t) = (5-((1*s(t))/40));

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a:=0;

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c:=5;

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init:=s(a)=c;

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b:=20;

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h:=2;

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g:=dsolve({de,init},{s(t)},type=numeric,method=classical[foreuler],startinit=true,stepsize=h);

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

g(b);

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The model is separable, so we can find the exact solution. Use Maple to find the exact solution.restart:with(DEtools):with(plots):

Warning, the name changecoords has been redefined

diffeq:=diff(s(t),t)=((200-s(t))/40);

NiM+SSdkaWZmZXFHNiIvLUklZGlmZkdJKnByb3RlY3RlZEdGKTYkLUkic0dGJTYjSSJ0R0YlRi4sJiIiJiIiIkYrIyEiIiIjUw==

s:='s';

NiM+SSJzRzYiRiQ=

diffeq;

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soln:=dsolve(diffeq,s(t));

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subs(_C1=1,soln);

NiMvLUkic0c2IjYjSSJ0R0YmLCYiJCsjIiIiLUkkZXhwRzYkSSpwcm90ZWN0ZWRHRi9JKF9zeXNsaWJHRiY2IywkRigjISIiIiNTRis=

soln1:=dsolve({diffeq,s(0)=0},s(t));

NiM+SSZzb2xuMUc2Ii8tSSJzR0YlNiNJInRHRiUsJiIkKyMiIiItSSRleHBHNiRJKnByb3RlY3RlZEdGMUkoX3N5c2xpYkdGJTYjLCRGKiMhIiIiI1MhJCsj

eqn:=5=subs(t=2,rhs(soln));

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c:=solve(eqn,_C1);

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subs(_C1=c,soln);

NiMvLUkic0c2IjYjSSJ0R0YmLCYiJCsjIiIiKiYtSSRleHBHNiRJKnByb3RlY3RlZEdGMEkoX3N5c2xpYkdGJjYjLCRGKCMhIiIiI1NGKy1GLjYjI0Y1IiM/RjUhJCY+

DEplot(diffeq,[s(t)],t=-100..1000,s=-1000..1000);

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DEplot(diffeq,[s(t)],t=-100..1000,s=-1000..1000,{[0,0]});

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Using the exact solution, find the amount of cranberry juice in the vat after 20 minutes.solu:=eval(soln1,t=20);

NiM+SSVzb2x1RzYiLy1JInNHRiU2IyIjPywmIiQrIyIiIi1JJGV4cEc2JEkqcHJvdGVjdGVkR0YxSShfc3lzbGliR0YlNiMjISIiIiIjISQrIw==

Another 200 gallon vat started out with 140 gallons of pure grape juice. In this vat, pure apple juice was added at 2 gallons per minute while thoroughly mixed juice was removed at 5 gallons per minute. Set up a model for this situation in Maple.restart:with(plots):

Warning, the name changecoords has been redefined

with(DEtools):v(t):=140+3*t;

NiM+LUkidkc2IjYjSSJ0R0YmLCYiJFMiIiIiRigiIiQ=

diffeq:=diff(a(t),t)=(5-((2*a(t))/(v(t))));

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Successful taste tests were conducted on a recipe concocted using juice drawn from this tank after 6 minutes. This new model is linear, so we can find the exact solution using the methods of Section 1.8. Have Maple find the exact solution.soln:=dsolve(diffeq,a(t));

NiM+SSVzb2xuRzYiLy1JImFHRiU2I0kidEdGJSwoIiRTIiIiIkYqIiIkKiYsJkYsRi1GKkYuIyEiI0YuSSRfQzFHRiVGLUYt

soln1:=dsolve({diffeq,a(0)=0},a(t));

NiM+SSZzb2xuMUc2Ii8tSSJhR0YlNiNJInRHRiUsKCIkUyIiIiJGKiIiJComLCZGLEYtRipGLiMhIiNGLkYsIyIiI0YuISRTIg==

Using the exact solution and Maple, determine the amount of apple juice in the vat after 6 minutes.amntofapplejuice:=eval(soln1,t=6);

NiM+STFhbW50b2ZhcHBsZWp1aWNlRzYiLy1JImFHRiU2IyIiJywmIiRlIiIiIiomRiwjRi0iIiQiJFMiIyIiI0YwIyEjcSIjeg==

What is the concentration of apple juice in the mixture in the vat after 6 minutes [Hiint: what is the total volume of juice in the vat after 6 minutes?]?volume:=eval(v(t),t=6);

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concentration:=(amntofapplejuice/volume);

NiM+SS5jb25jZW50cmF0aW9uRzYiLywkLUkiYUdGJTYjIiInIyIiIiIkZSIsJkYtRi0qJkYuI0YtIiIkIiRTIiMiIiNGMiMhI04iJVRp

In another experiment, we start again with one 200 gallon vat full of pure apple juice and one 200 gallon vat containing 140 gallons of pure grape juice. In the first vat (starting full of apple juice) we are still adding pure cranberry juice at 5 gallons per minute and removing thoroughly mixed juice at 5 gallons per minute. In the second vat, we are still adding pure apple juice at 2 gallons per minute and removing thoroughly mixed juice at 5 gallons per minute, but now we are also letting the apple-cranberry outflow from the first vat flow into the second vat. Set up a system of two equations using only two dependent variables, the first one modeling the amount of cranberry juice in the first vat and the second one modeling the amount of apple juice in the second vat [Hints: 1) The juice in the first vat is not affected by where its outflow goes. 2) The first vat has a constant volume of 200 gallons of mixed apple and cranberry juice, so you can express the amount of apple juice in the first vat as a function of the amount of cranberry juice in the first vat.]restart:with(plots):

Warning, the name changecoords has been redefined

with(DEtools):diffeq:=diff(c(t),t)=(5-((5*c(t))/(200)));

NiM+SSdkaWZmZXFHNiIvLUklZGlmZkdJKnByb3RlY3RlZEdGKTYkLUkiY0dGJTYjSSJ0R0YlRi4sJiIiJiIiIkYrIyEiIiIjUw==

solnc:=dsolve({diffeq,c(0)=0},c(t));

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v(t):=140+(8*t);

NiM+LUkidkc2IjYjSSJ0R0YmLCYiJFMiIiIiRigiIik=

diffeq1:=diff(c(t),t)=(-5*(e^(-t/40)));

NiM+SShkaWZmZXExRzYiLy1JJWRpZmZHSSpwcm90ZWN0ZWRHRik2JC1JImNHRiU2I0kidEdGJUYuLCQpSSJlR0YlLCRGLiMhIiIiI1MhIiY=

solna:=dsolve({diffeq1,c(0)=200},c(t));

NiM+SSZzb2xuYUc2Ii8tSSJjR0YlNiNJInRHRiUsJiomLUkjbG5HNiRJKnByb3RlY3RlZEdGMEkoX3N5c2xpYkdGJTYjSSJlR0YlISIiKUYzLCRGKiNGNCIjUyIiIiIkKyMqJiwmRjRGOUYtRjlGOUYtRjRGOg==

system1:=[diff(c(t),t)=5-c(t)/40,diff(b(t),t)=5*(200-c(t))+5-(2*b(t)/v(t))];

NiM+SShzeXN0ZW0xRzYiNyQvLUklZGlmZkdJKnByb3RlY3RlZEdGKjYkLUkiY0dGJTYjSSJ0R0YlRi8sJiIiJiIiIkYsIyEiIiIjUy8tRik2JC1JImJHRiVGLkYvLCgiJTA1RjJGLCEiJiomRjlGMiwmIiRTIkYyRi8iIilGNCEiIw==

Have Maple create a graph of the solution curve in the phase plane for the solution to this system with the given initial conditions DEplot(system1,[c(t),b(t)],t=0..200,{[c(0)=0,b(0)=0]});

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Have Maple create a time series graph for the amount of cranberry juice in the first tank as a function of time. DEplot(diffeq,[c(t)],t=0..200,c=0..200,{[0,0]});

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