Asolve the lp problem if no optimal solution exists indicate...

A.) Solve the LP problem. If no optimal solution exists, indicate whether the feasible region is empty or the objective function is unbounded. (Enter EMPTY if the region is empty. Enter UNBOUNDED if the function is unbounded.) Maximize p = 3x + 2y subject to -2x + y ≥ 5, x + 5y ≤ 7, x ≥ 0, y ≥ 0. B.) Solve the LP problem. If no optimal solution exists, indicate whether the feasible region is empty or the objective function is unbounded. (Enter EMPTY if the region is empty. Enter UNBOUNDED if the function is unbounded.) Minimize c = 2x + 4y subject to 0.9x + 0.9y ≥ 9, x + 2y ≥ 14, x ≥ 0, y ≥ 0.

Transcript

00:01 So in this problem, we have this linear programming model.

00:05 We're asked to solve this if any solution exists.

00:09 And if not, if there's no solution, then we'll list that, or if the objective function is unbounded.

00:21 We're supposed to indicate that.

00:24 And if the region is empty, in other words, there's no solution that occurs.

00:28 So the first one we have is that we're trying to maximize p equal to 3x plus 2 .1.

00:34 Subject to these constraints negative 2x plus y is greater than equal to 5 x plus 5 y is less than equal to 7 and x is greater than equal to 0 and y is greater than equal to 0 so we'll make a table over x and y is that satisfy these constraints and calculate the p first of all we need to graph these constraints and see where the feasible region is right that'll be bounded by these constraints so we'll do the first one i went to desmos .com, first of all.

01:08 Brought down my graphing calculator.

01:10 And so we'll enter the first constraint here.

01:12 Negative 2x plus y.

01:15 So i have negative 2x plus y is greater than or equal to 5.

01:34 5.

01:36 Okay? which is that zone up there.

01:39 And then the next one, x plus 5 y less than equal to 7.

01:43 So i have x.

01:45 Oops, i want a small x plus 5y is less than or equal to 7.

02:06 Gives us that zone there.

02:10 Okay.

02:11 And we want x greater than zero...