Class 12 Linear Programming · Case Study4 Markslinear_programming_models
Class 12 Maths · Linear Programming · Case Study #75
For a mathematical investment model, at most ₹12000 is split between A and B, with at least ₹2000 in A and ₹4000 in B. Assume fixed annual returns of 8% and 10%, respectively. Let x,y denote rupees allocated to A,B.
Part (1) 2 Marks
Formulate the LPP for maximum annual return.
Answer: Maximize Z=0.08x+0.10y; x≥2000,y≥4000,x+y≤12000.
- The annual return equals 8x/100+10y/100.
- The minimum allocations are x≥2000,y≥4000, while the total budget imposes x+y≤12000.
- Maximize Z=0.08x+0.10y subject to those constraints.
Part (2) 2 Marks
Find the allocations maximizing annual return.
Answer: A: ₹2000; B: ₹10000; return ₹1160.
- The feasible triangle has vertices (2000,4000),(8000,4000),(2000,10000).
- Annual returns are ₹560,₹1040,₹1160, respectively.
- Thus allocate ₹2000 to A and ₹10000 to B for modelled annual return ₹1160.