A bank has set aside a maximum of S50 million dollars for commercial and home lo

Question

A bank has set aside a maximum of S50 million dollars for commercial and home loans. Every million dollars in commercial loans requires 1 application form while every million dollars in home loans requires 2 forms. The bank cannot process more than 96 forms at this time. The bank's policy is to loan at least four times as much for home loans as for commercial loans. At least S10 7. Or 12% on home loans. What amount of money should bc alloted for each type of loan to maximize the interest income? The bank should allot Smillion for commercial loans and Smillion for home loans (Type an integer or decimal rounded to two decimal places as needed.) (Type an integer ordecimal remark will earn iss/-] million (Type an integer or decimal rounded to two decimal places as needed.)

Explanation / Answer

According to the question

At least four times as much for home loan as compare to commercial loans therfore

Let

x millions for commercial loans

4x millions for home loans are being invested

Because on the basis of total amount invested in the Commercial loan and home loan is $10 millions .

x+4x = $10

5x = $10

x = $2

Commercial loans ammount is $2 millions

Home loan invested amount is 4× 2 = $8 millions

By the principal values ratio of investment is 1:4

Therfore $50 millions can be distributed in this

Ratio 50 × 1/5 = $10 millions amount of commercial loans .(with 10 application)

50 × 4/5 = $40 million amount of home loans(with 80 application)

Total application counted 90

Maximum Earning by commercial loans is = 10 × 10/100 = $1 millions

Maximum earning by home loans is = 40 × 12/100 = $4.8 millions

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