Problem $1,2-11($Algorithmic$)$

Consider the problem

Min $2x^2-15x+2xY+Y^2-20Y+65$

$s.t.x+3Y10$

a$.$ Find the minimum solution to this problem. If required, round your answers to two decimal places.

The optimal solution is $x=Y=$ for an optimal solution value of

b$.$ If the right$-$hand side of the constraint is increased from $10$ to $11,$ how much do you expect the objective function to change? If required, round your answer to two decimal places.

The optimal objective function value will iby

c$.$ Re$-$solve the problem with a new right$-$hand side of $11.$ How does the actual change compare with your estimate? If required, round your answers to two decimal places.

The new optimal objective function value is so the actual is