Enter the number with digits, not in letters. For example: enter $10,$ not Ten.

If there is a fraction to the number, do not enter unnecessary zeros. For example: enter $12\mathrm{.}5,$ not $12\mathrm{.}50.$

If there are more than two digits in the fraction, enter the first two. For instance, if your answer is $\frac{1}{3},$ enter $0\mathrm{.}33$ and if it is

$\frac{2}{3},$ enter $0\mathrm{.}66.$

Do not enter commas. For example: enter $3850,$ not $3,850.$

Do not enter any extra spaces or other characters.

Questions are graded automatically. If you do not follow the formatting, then your answer will be graded wrong. If your answer is

correct, I will be able to manually change your grade for those questions later, but you will lose $25\%$ of the points. NO

EXCEPTIONS, in order to be fair to everyone in the class.$)$

Consider the following linear programming.

Minimize $3x+2Y$

Subject $tox+Y4$

$,x+2Y6$

$,4x+Y7$

$,x0$

$,Y1$

Draw the plot for the feasible region.

The set of feasible solutions for this linear programming has

feasible corner points. $($Enter the number of

feasible corner points$)$

The objective value for the optimal corner point is

The objective value for the second$-$best corner point is

Suppose I start decreasing the coefficient of $x$ in the objective function $($currently $3).$ What is the value of the coefficient at which the

current second$-$best corner point becomes an optimal solution? Enter your answer here:

$.($You need to enter

the value of the new coefficient, NOT the change NOR the value of objective.$)$