1. // state the general forms with solved examples of your choice forms of yp particular integral in the non homogenous differential equations[10mks]
2. three grams of a radio active isotope decay in two weeks to 0.9 grams .Determine both the half life and constant of proportionality [8mks]
3. using the artificial variable technique solve

Min Z=5x1+3x2

subject to

2x1+4x2 less than or equal to12

2x1+2x2 =10

5x1+2x2 greater than or equal to 10

and x1=x2 greater than or equal to zero.

write the above in standard using mathematical approach.

4.a conservative investor has 100000 dollars to invest ,the investor has decided to use three ways for generating income ,municipal bonds

certificate of deposits

money markets account

after reading a financial news letter the investor also identified several additional restrictions on the investment

1.no more than 40%shold be on bonds

2.the proportion allocated to money markets account should be at least double the amount on certificate deposit

the annual return will be 8% on bonds ,9% on certificate of deposit ,7% on money markets .Assume the entire amount will be invested .formulate the linear programing

model ignoring any transaction cost and the potential of different investment lines

explain and develop a linear programming model of the above ?