Question

TV company makes 2 models A and B. - A takes 4 hrs to make, B takes 2 hrs
- Max 1000 hrs available
- Profit per unit: A → ₹1200, B → ₹800
- Want to maximize profit under constraints

• A. 200 model As and 400 model Bs
• B. 100 model As and 600 model Bs
• C. 800 model Bs
• D. None of the above

Hint:

Form linear equation from constraint and profit function. Check if profit increases or decreases with x and optimize accordingly.

Answer 1

The Correct Option is B

Let \( x \) = model A, \( y \) = model B

Constraints:
- \( 4x + 2y \leq 1000 \)
- Maximize: \( P = 1200x + 800y \)

Try (a): \( x = 200, y = 400 \)
→ \( 4(200) + 2(400) = 800 + 800 = 1600 \) ✗ (Exceeds)

Try (b): \( x = 100, y = 600 \)
→ \( 400 + 1200 = 1600 \) ✗ (Exceeds)

Try (c): \( x = 0, y = 800 \)
→ \( 0 + 1600 = 1600 \) ✗ (Exceeds)

Now try satisfying the constraint exactly:
\[ 4x + 2y = 1000 \Rightarrow 2x + y = 500 \Rightarrow y = 500 - 2x \]
Substitute into the profit function:
\[ P = 1200x + 800y = 1200x + 800(500 - 2x) = 1200x + 400000 - 1600x = 400000 - 400x \]

This is decreasing in \( x \) ⇒ maximum occurs at minimum \( x \)
So set \( x = 0, y = 500 \Rightarrow \boxed{P = 800 \times 500 = 400000} \)

Correct Answer: (d) None of the above is correct.