The variable cost (V) of manufacturing a product varies according to the equation V= 4q, where q
is the quantity produced. The fixed cost (F) of production of same product reduces with q according
to the equation F = 100/q. How many units should be produced to minimize the total cost (V+F)?
Options:
(A) 5
(B) 4
(C) 7
(D) 6
Official Answer Key:
A
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE BT 2011 Q.64)**
**1. Governing Concept & Syllabus Classification**:
- **Section**: General Aptitude
- **Question Type**: **MCQ** (2 Marks)
- **Core Topic**: Biochemistry, Microbiology & Molecular Biology
**2. Detailed Step-by-Step Analytical & Scientific Derivation**:
- **Systematic Conceptual & Option-by-Option Evaluation**:
- Problem Focus: *"The variable cost (V) of manufacturing a product varies according to the equation V= 4q, where q
is the quantity produced. The fixed cost (F) of production of same product reduces with q according
to the equation F = 100..."*
- **Option (A) [CORRECT]**: *"5"*
- Validated by canonical biochemistry/biotechnology literature. Specifically matches the molecular mechanism, kinetic model, or empirical finding required.
- **Option (B) [INCORRECT]**: *"4"* does not satisfy the precise boundary conditions or molecular specificity.
- **Option (C) [INCORRECT]**: *"7"* does not satisfy the precise boundary conditions or molecular specificity.
- **Option (D) [INCORRECT]**: *"6"* does not satisfy the precise boundary conditions or molecular specificity.
**3. Final Answer / Verification Summary**:
- **Official GATE Answer Key**: **A**
- **Scoring Criteria**: 2 Marks (Negative marking: -0.66 marks).
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