Thriftem Bank is in the process of devising a loan Policy that involves a maximu

Question

Thriftem Bank is in the process of devising a loan Policy that involves a maximum of $12 million. The following table provides the pertinent data about available types of loans. Bad debts are unrecoverable and produce no interest revenue. Competition with other financial institution requires that the bank allocate at least 40% of the funds to farm and commercial loans. To assist the housing industry in the region, home loans must equal at least 50% of the personal, car, and home loans. The bank also has a stated policy of not allowing the overall ratio of bad debts on all loans to exceed 4%. The situation seeks to determine the amount of loan in each category. Formulate the problem as a LP problem.

Explanation / Answer

Let x1, x2, x3, x4, x5 (in million dollars) be the amount of funds allocated to Personal loan, Car loan, Home loan, Farm loan and Commercial loan respectively.

Net return:

• Personal: (0.9x1) (0.14) 0.1x1 = 0.026x1

• Car: (0.93x2) (0.130) 0.07x2 = 0.0509x2

• Home: (0.97x3) (0.120) 0.03x3 = 0.0864x3

• Farm: (0.95x4) (0.125) 0.05x4 = 0.06875x4

• Commercial: (0.98x5) (0.100)0.02x5 = 0.078x5

Total Fund:

X1 + x2 + x3 + x4 + x5 12

Competition:

X4 + x5/ x1 + x2 + x3 + x4 + x5 0.4

0.4x1 + 0.4x2 + 0.4x3 0.6x4 + 0.6x5 0

Housing industry:

X3 0.5(x1+x2+x3) 0.5x1+0.5x20.5x3 0

Overall bad debt:

0.1x1 + 0.07x2 + 0.03x3 + 0.05x4 + 0.02x5/ x1 + x2 + x3 + x4 + x5 0.04

0.06x1+0.03x20.01x3+0.01x40.02x5 0

The LP formulation:

Maximize=0.026x1 + 0.0509x2 + 0.0864x3 + 0.06875x4 + 0.078x5

Subject to:

x1 + x2 + x3 + x4 + x5 12

0.4x1 + 0.4x2 + 0.4x3 0.6x4 + 0.6x5 0

0.5x1 + 0.5x2 0.5x3 0

0.06x1 + 0.03x2 0.01x3 + 0.01x4 0.02x5 0

x1, x2, x3, x4, x5 0

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