Linear Programming HELP NEEDED PLEASE!

Start by writing your equations:

X = amount for personal loans
Y = amount for car loans

1) X+Y = 200,000
2) Return after one year = X (1.14)(1-.03) + Y (1.12)(1-.02)
3) Y>=X

Combine 1 and 2. Find where three intersects the combination. That is the optimal allocation. The rate of return of all loans is the answer to equation 2 divided by the starting amount (200,000)

Let C be personal Loans and P be personal loans
You've got two constraints
C+P<=200K
and
P<=C
Plot these up on a C&P coordinate axis as
C+P<=200K
and C>=P
the Feasible Regions are under C+P=200K line and above the C=P line

Where C=P intersects C+P=200K, is the optimum withing the Feasibility region. or C=100K and P=100K

The return on these loans is
Pr=P(1-0.03)(1+0.14)=P(1.1058) return on P is 10.58%
Cr=C(1-0.02)(1+0.12)=C(1.0976) return on C is 9.76%

Expected Return on $200K is [P(0.1058)+C(0.0976)]/(P+C)
and since P=C the optimum is 10.17%

plus the repossessed cars

Rap

Re: Linear Programming HELP NEEDED PLEASE!

Does that define a boundary condition for the optimal allocation, or does it just describe the bank's usual behavior? If the optimal allocation is different from what the bank usually does, would that make it non-optimal? Or would it merely mean that the bank mismanaged its business in the past?

Thanks very much!