Subject: Computer Programming

Q $1$: According to a dietician, a person should consume exactly $200$ gm of carbohydrates, at

least $175$ gm of proteins and at most $150$ gm of fats in a meal. The dietician also recommends

to have as much amount of vitamins as possible. The three food items that the person eats has

$80,65$ and $30$ gm of carbohydrates per kilogram of food item. The same food items contain $10,$

$12,23$ gm of proteins in each kilogram. Per kilogram of the same food items comprise of $32,$

$56$ and $42$ gm of fats. Vitamins contained in per kilogram of the same food items are $70,37$

and $58$ gm $.$

Determine how much kilogram of each food item the person should consume so as to have

maximum intake of vitamins by using appropriate built$-$in function present in MATLAB.

Q $2$: The following data is obtained from an experiment aimed at measuring the spring constant

of a given spring. Different masses m are hung from the spring and the corresponding

deflections $$ of the spring from its upstretched configuration are measured. From physics, we

know that $F=k$ and here $F=mg.$ Thus, we can find k from the relationship $k=m\frac{g}{}.$ Here,

however, we are going to find k by plotting the experimental data, fitting the best straight line

through the data, and then measuring the slope of the best$-$fit line.

Write the MATLAB script that shows the steps involved in making a straight line fit through

the given data in the spring experiment and finding the spring constant.

$($Hint: use the polyfit and polyval function$)$

Q $3$: Question:

In a coal$-$fired power plant, operating on Carnot Cycle, it is possible to set any value for the

temperature of boiler in which heat is added to water at high temperature $(T_H)$ and any value

for the temperature of condenser in which heat is rejected from steam at low temperature $(T_C),$

from the following temperature list

$T=\left[\begin{array}{cccccccccccc}500& 320& 1000& 775& 385& 670& 845& 1245& 410& 300& 627& 514\end{array}\right]K$

Being an operator of power plant you have to select $T_H$ and $T_C$ from the above temperature list

so that power plant operates at its highest efficiency.

Write a generalized MATLAB program to select two temperature values $T_H$ and $T_C$ for above

condition, without using min and max built$-$in function.

Print the maximum efficiency of cycle and the temperatures at which it occurs.