Question

please provide matlab solution too

3. Butterball recommends the following cooking times for turkeys at 325 °C. size, (lbs) un-stuffed t, (h) stuffed t, (h) 2.00 2.25 6. 2.50 2.75 10 3.00 3.50 18 3.50 4.50 22 4.00 5.00 24 4.50 5.50 30 5.00 6.25 (a) Plot the recommended cooking time as a function of turkey size for un-stuffed and stuffed turkeys on the same plot. (b) For each of the two menu options, find the third-order interpolating polynomial (by either the Newton or the Lagrange method) using the points at 7, 10, 18, and 22 Ibs. Add these polynomials to the plot in (a). For plotting the polynomials, use 30 data points between 7 and 22 lbs only, to get a smooth curve. (c) Find the recommended cooking times for a 15-lb turkey (stuffed and un-stuffed) using your interpolating polynomials.

Answer 1

THE CODE FOR THE ABOVE QUESTION IS :

function main()

sizelbs = [6, 7, 10, 18, 22, 24, 30];
unstuffed = [2.00, 2.50, 3.00, 3.50, 4.00, 4.50, 5.00];
stuffed = [2.25, 2.75, 3.50, 4.50, 5.00, 5.50, 6.25];

% (a)
% plotting the given data
plot(sizelbs, unstuffed);
title('Cooking time for turkeys at 325°C');
hold on

plot(sizelbs, stuffed);
hold on

% (b)
% x will hold 30 points from 7 to 22
x = linspace(7,22,30);

% y1 is the interpolated data for unstuffed turkey
y1 = zeros(1,length(x));
for i = 1:length(x)
y1(i) = LagrangeInterp([7 10 18 22],[2.50 3.00 3.50 4.00],x(i));
end

% plotting the data obtained
plot(x,y1,'--');
hold on

% y2 is the interpolated data for stuffed turkey
y2 = zeros(1,length(x));
for i = 1:length(x)
y2(i) = LagrangeInterp([7 10 18 22],[2.75 3.50 4.50 5.00],x(i));
end

plot(x,y2,'--');
hold on

% (c)
% getting the value from the plotted points the value at x = 15 for
% stuffed and unstuffed turkey
stuffed15lbs = interp1(x,y1,15);
unstuffed15lbs = interp1(x,y2,15);

% plotting the points obtained and printing them also
plot(15,stuffed15lbs,'o');
hold on
plot(15,unstuffed15lbs,'o');

legend('Unstuffed','Stuffed','Unstuffed Interpolated','Stuffed Interpolated','Recommended cooking time for stuffed turkey 15lbs','Recommended cooking time for unstuffed turkey 15lbs');
xlabel('size (lbs)');
ylabel('time (h)');
hold off

fprintf('The recommended time for 15lbs stuffed and unstuffed turkey is %fh and %fh respectively.\n',stuffed15lbs,unstuffed15lbs);
end

function yi = LagrangeInterp(x,y,xi)

n = length(x);
L = zeros(1,n);

for i = 1:n
L(i) = 1;
for j = 1:n
if j ~= i
L(i) = L(i)*(xi-x(j))/(x(i) - x(j));
end
end
end
yi = sum(y.*L);
end

SCREENSHOT OF CODE :

main.m function main () [6, 7, 10, 18, 22, 24, 30]; sizelbs = unstuffed = [2.00, 2.50, 3.00, 3.50, 4.00, 4.50, 5.00]; stuffed = [2.25, 2.75, 3.50, 4.50, 5.00, 5.50, 6.25]; * (a) * plotting the given data plot (sizelbs, unstuffed) ; title ('Cooking time for turkeys at 325°C'); 10 hold on 11 12 plot (sizelbs, stuffed); 13 14 - hold on 15 16 17 * (b) $ x will hold 30 points from 7 to 22 x = linspace (7,22,30); 18 19 20 21 * yl is the interpolated data for unstuffed turkey yl = zeros (1,length (x) ); É for i = 1:length (x) 22 23 24 LagrangeInterp ([7 10 18 22], [2.50 3.00 3.50 4.00],x(i)): 25 yl (i) 26 end 27 * plotting the data obtained plot (x, yl,'--'); 28 29 hold on 30 31 * y2 is the interpolated data for stuffed turkey zeros (1,length (x)); for i = 1:length (x) y2 (i) = LagrangeInterp ([7 10 18 22], [2.75 3.50 4.50 5.00],x(i)): 32 33 y2 = 34 35 36 - end 37 plot (x, y2,'--'); 38- hold on 39 - 40 41 42 * (c) $ getting the value from the plotted points the value at x = 15 for * stuffed and unstuffed turkey 43 44 45 interpl (x, yl,15); interpl (x, y2,15); 46 - stuffedl5lbs = 47 - unstuffed15lbs 48


$ plotting the points obtained and printing them also plot (15, stuffed15lbs,'o'); 49 50 hold on 51 - plot (15, unstuffed15lbs, 'o'); 52 - 53 legend ('Unstuffed', 'Stuffed', 'Unstuffed Interpolated', 'Stuffed Interpolated', 'Recommended cooking time for stuffed turkey 151bs', 'Recommended cooking time for unstuffed turkey 151bs'); xlabel ('size (lbs) ') ; 54 55 56 ylabel ('time (h) '); 57 hold off 58 fprintf('The recommended time for 15lbs stuffed and unstuffed turkey is &fh and $fh respectively.\n',stuffed15lbs, unstuffed15lbs); 59 - 60 - end 61 + function yi = LagrangeInterp (x, y,xi) 62 77 78 79


OUTPUT :

>> main The recommended time for 15lbs stuffed and unstuffed turkey is 3.337144h and 4.204295h respectively. >>

Cooking time for turkeys at 325°C 6.5 Unstuffed Stuffed Unstuffed Interpolated Stuffed Interpolated 6 Recommended cooking time for stuffed turkey 15lbs Recommended cooking time for unstuffed turkey 15lbs 5.5 5 4.5 3.5 3 2.5 20 25 30 10 15 size (Ibs) time (h)