Question

1. Max 2X1 + 3X2

s.t. 6X1 + 3X2 < 18 (1)

4X1 + 8X2 < 32 (2)

1X1 + 2X2 > 2 (3)

X1 > 1 (4)

X1, X2 > 0
Draw the boundary straight line for each constraint. Must show the points used (or slope/Intercept if used).

Answer 1

To draw the boundary straight lines for each constraint in the given linear programming problem, rewrite each constraint in the form of y = mx + b. Then, plot the lines using the slope-intercept form.

Step-by-step explanation:

To draw the boundary straight lines for each constraint, we need to rewrite each constraint in the form of y = mx + b, where m is the slope and b is the y-intercept. Let's rewrite the constraints:

1. 6X1 + 3X2 < 18 → 3X2 < -6X1 + 18 → X2 < -2X1 + 6
2. 4X1 + 8X2 < 32 → 8X2 < -4X1 + 32 → X2 < -0.5X1 + 4
3. 1X1 + 2X2 > 2 → 2X2 > -X1 + 2 → X2 > -0.5X1 + 1
4. X1 > 1

Now, let's plot these boundary lines:

1. The line for constraint (1) has a slope of -2 and a y-intercept of 6.

2. The line for constraint (2) has a slope of -0.5 and a y-intercept of 4.

3. The line for constraint (3) has a slope of -0.5 and a y-intercept of 1.

4. The line for constraint (4) is a vertical line passing through the point (1, 0).