Question

You can collect as many rubies and emeralds as you can. Each ruby is worth Rs. 4 crore and each emerald is worth Rs. 5 crore. Each ruby weighs 0.3 kg and each emerald weighs 0.4 kg. Your bag can carry at most 12 kg. What should you collect to get the maximum wealth?

• A. 20 rubies and 15 emeralds
• B. 40 rubies
• C. 28 rubies and 9 emeralds
• D. None of these

Hint:

For optimization problems like this, use trial and error with the given constraints to find the maximum possible value.

Answer 1

The Correct Option is B

Let the number of rubies be \( r \) and the number of emeralds be \( e \). The total weight of rubies and emeralds is: \[ 0.3r + 0.4e \leq 12. \] We want to maximize the total value: \[ \text{Value} = 4r + 5e. \] Using trial and error: - If \( r = 40 \), the total weight is \( 0.3 \times 40 = 12 \), so the bag is full. The value is \( 4 \times 40 = 160 \). - If \( r = 20 \) and \( e = 15 \), the weight is \( 0.3 \times 20 + 0.4 \times 15 = 6 + 6 = 12 \), and the value is \( 4 \times 20 + 5 \times 15 = 80 + 75 = 155 \). Thus, the maximum wealth is obtained by taking 40 rubies.