The cost function for a product i n a firm is given by 5q2, where q is the amount of production. The
firm can sell the product at a market price of
50 per unit. The number of units to be produced by
the firm such that the profit is maximized is
(A) 5 (B) 10 (C) 15 (D) 25
Options:
(A) 5
(B) 10
(C) 15
(D) 25
Official Answer Key:
A
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE BT 2012 Q.56)**
**1. Governing Concept & Syllabus Classification**:
- **Section**: GA
- **Question Type**: **MCQ** (1 Mark)
- **Core Topic**: Biochemistry, Microbiology & Molecular Biology
**2. Detailed Step-by-Step Analytical & Scientific Derivation**:
- **Systematic Conceptual & Option-by-Option Evaluation**:
- Problem Focus: *"The cost function for a product i n a firm is given by 5q2, where q is the amount of production. The
firm can sell the product at a market price of
50 per unit. The number of units to be produced by
the firm such tha..."*
- **Option (A) [CORRECT]**: *"5"*
- Validated by canonical biochemistry/biotechnology literature. Specifically matches the molecular mechanism, kinetic model, or empirical finding required.
- **Option (B) [INCORRECT]**: *"10"* does not satisfy the precise boundary conditions or molecular specificity.
- **Option (C) [INCORRECT]**: *"15"* does not satisfy the precise boundary conditions or molecular specificity.
- **Option (D) [INCORRECT]**: *"25"* does not satisfy the precise boundary conditions or molecular specificity.
**3. Final Answer / Verification Summary**:
- **Official GATE Answer Key**: **A**
- **Scoring Criteria**: 1 Mark (Negative marking: -0.33 marks).
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