Scilab Code Solutions

Practice Problems

1. Retail Store: Discount Calculator

A retail store offers a discount based on the total purchase amount:

• 10% if the amount is between ₹500 and ₹1000.

• 20% if the amount is above ₹1000.

Write a Scilab script to calculate the final amount after discount for a given purchase amount.

// Input purchase amount

amount = input("Enter the purchase amount: ");

// Calculate discount

if amount > 500 & amount <= 1000 then

discount = 0.10* amount;

elseif amount > 1000 then

discount = 0.20 amount;

else discount = 0;

end

// Final amount

final_amount = amount - discount;

disp("Final amount after discount: "), disp(final_amount);

2. Factory Production: Matrix Analysis

A factory produces 3 types of products (A, B, C) in 3 shifts (morning, afternoon, evening).
The production quantities are as follows:
Morning: [50, 60, 70], Afternoon: [40, 50, 60], Evening: [30, 20, 10].

Find:

• Total production for each product.

• Total production for each shift.

3. Finance: Compound Interest Calculation

You invest ₹10,000 in a savings account that offers an annual interest rate of 5%.

Write a Scilab script to compute the amount after 10 years, assuming the interest compounds annually.

// Production matrix

production = [50 60 70; 40 50 60; 30 20 10];

// Total production for each product

product_total = sum(production, "r");

disp("Total production for each product: "), disp(product_total);

// Total production for each shift

shift_total = sum(production, "c");

disp("Total production for each shift: "), disp(shift_total);

// Inputs

P = 10000; // Principal amount

r = 5/100; // Annual interest rate

n = 10; // Time in years

// Compound interest formula

A = P * (1 + r)^n;

disp("Amount after 10 years: "), disp(A);

4. Data Science: Exam Analysis

The scores of 5 students in a Math exam are: [78, 85, 62, 90, 88].

Calculate:

• The average score.

• The highest and lowest scores.

• Whether the average score qualifies as "pass" (cutoff: 50).

// Scores

scores = [78, 85, 62, 90, 88];

// Average score

avg_score = mean(scores);

// Highest and lowest scores

max_score = max(scores);

min_score = min(scores);

// Pass/fail decision

if avg_score >= 50 then

result = "Pass";

else

result = "Fail";

end

disp("Average score: "), disp(avg_score);

disp("Highest score: "), disp(max_score);

disp("Lowest score: "), disp(min_score);

disp("Result: "), disp(result);

5. Engineering: Voltage-Current Relationship

In a circuit, the voltage V across a resistor is related to the current I by Ohm's law:

V = IR

If R = 10 Ω, and the current varies as [1, 2, 3, 4, 5] amperes, compute the corresponding voltage values.

// Resistance

R = 10;

// Current values

I = [1, 2, 3, 4, 5];

// Voltage calculation

V = I * R;

disp("Voltage values: "), disp(V);

6. Environment: Rainfall Statistics

A city records the monthly rainfall (in mm) for 6 months as: [120, 85, 95, 110, 140, 75].

• Find the total rainfall over 6 months.

• Compute the average monthly rainfall.

• Determine which month had the highest and lowest rainfall.

// Rainfall data

rainfall = [120, 85, 95, 110, 140, 75];

// Total rainfall

total_rainfall = sum(rainfall);

// Average rainfall

avg_rainfall = mean(rainfall);

// Highest and lowest rainfall

[highest, highest_month] = max(rainfall);

[lowest, lowest_month] = min(rainfall);

disp("Total rainfall: "), disp(total_rainfall);

disp("Average monthly rainfall: "), disp(avg_rainfall);

disp("Month with highest rainfall: "), disp(highest_month);

disp("Month with lowest rainfall: "), disp(lowest_month);

7. Physics: Projectile Motion

A ball is thrown with an initial velocity u = 20 m/s at an angle of 45°.

Write a Scilab script to compute and plot the trajectory of the ball. Use g = 9.81  .

// Parameters

u = 20; // Initial velocity

theta = 45 * %pi / 180; // Convert angle to radians

g = 9.81; // Gravitational acceleration

// Time of flight

T = (2 u sin(theta)) / g;

// Time intervals

t = linspace(0, T, 100);

// Trajectory equations

x = u cos(theta) t;

y = u sin(theta) t - (0.5 g t.^2);

// Plot trajectory

plot(x, y);

xlabel("Horizontal Distance (m)");

ylabel("Vertical Distance (m)");

title("Projectile Motion");