$1.$ Washwell Consumer Products is desirous of raising funds aggregating Rs$.5$ crores for financing a new plant for the manufacture of detergents. The project is to be set up in an industrially backward area and it would be possible to obtain some funding from a Development Financial Institution. Washwell is also considering funding options from two other sources, viz term loan from a commercial bank or issue of bonds. The rate of interest of the three options is given below:

From Interest rate

Development Financial Institution $12\%$

Bank $16\%$

Bonds $14\%$

The Finance Director is in the process of deciding on a funding mix. He however has some stipulations. Considering the repayment schedule of loans and the cash flows in the project, he would like the amount to be raised from the Development Finance Institution and bank not to exceed $75\%$ of the total fund requirement. The amount from FI should be at least Rs$.50$ lakhs more than bank, considering the interest differential. As the issue of bonds requires a lumpsum at the time of redemption, he would like to limit the amount to a maximum of $20\%$ of the aggregate amount. Formulate this as an LP problem to determine the funding pattern which will minimize the overall interest outgo.