Problem $3$

Consider the following deterministic optimization problem:

Minimise

$q,f(x_1,x_2)=0\mathrm{.}25x_1^2+x_2^2$

Subject to:

$(x_1,x_2)=5-x_1-x_2=0$

$g(x_1,x_2)-=x_1+0\mathrm{.}2x_2-30$

Now, assume that the $0\mathrm{.}25$ coefficient that appears in the objective function represents an uncertain

parameter. Let's call this parameter $C.$ The scenarios for the value of $C$ and corresponding

probability are given in the table below.

Formulate the above problem as a stochastic program. Assume that $x1$ and $x2$ are both here$-$and$-$

now decision variables.

Problem $4$

Again, consider the deterministic problem given in Problem $3.$

Assume that the $0\mathrm{.}25$ coefficient that appears in the objective function represents an uncertain

parameter. Let's call this parameter $C.$ The scenarios for the value of $C$ and corresponding

probability are given in the table above $($see Problem $3).$

Also, assume that the $3$ that appears in the inequality constraint represents an uncertain parameter.

Let's call this parameter D$.$ The scenarios for the value of D and corresponding probability are

given in the table below

a$)$ Construct a scenario tree.

b$)$ Formulate the problem as a stochastic program. Assume that $x1$ and $x2$ are both here$-$and$-$

now decision variables.