00:01
Hello everyone.
00:03
So part a in part a of the equation, we have to write a linear program.
00:10
So linear program is a mathematical model with a linear objective function and a set of linear constraints where variables are non -negative.
00:18
Here, let us assume two variables s and m where s denotes the number of units purchased.
00:28
Number of units purchased in stock fund whereas m represents the number of units purchased in money market fund now as per the given information a linear model becomes this is our objective function which is represented by z objective function which is minimize 8 s plus 3m now these are our constraints, these three are constraints based on available funds, annual income and market fund minimum respectively.
01:31
This is a non -negative constraint.
01:33
It is also a constraint but specifically it is called non -negative constraint.
01:42
Why? because in linear programming problem, we assume that our variables are non -negative.
01:49
Now to write the program we use lingo programming programming.
02:02
So code lines using lingo programming becomes minimize m i .n equals 8 s plus 3 multiplied by m writing the constraints 50 multiplied by s plus 100 multiplied by m less than equals to 1 -2 -0 -0 -0 -0.
02:33
Further, 5 s plus 4m, okay, less than equals to is written as less than sign first and then equals to sign.
02:53
Similarly greater than equals to 60 ,000.
02:59
Next, m greater than equals to 3 ,000.
03:04
We do not write non -negative constant in this case for in case of lingot programming, finally we write end.
03:15
Right.
03:17
Now we click on solve button.
03:19
So this gives the optimal solution.
03:27
This gives the optimal solution which will be s equals to 4 ,000 and m equals to 10 ,000...