Question

Given the following LP model: Max 5X1+ 4X2 s.t. 10X1+8X2 <= 40 (1) X1 + 4X2 <=8 (2) X1 , X2 >= 0

1) Please figure out the slopes of each constraint boundary line (Assume that X1 is the horizontal axis and X2 is the vertical axis).

2) Generally speaking, what type of LP models (with two decision variables) will have multiple optimal solutions?

3) Are there multiple optimal solutions for this LP model? Why?

Answer 1

To find the slopes of the constraint boundary lines in this LP model, rearrange each constraint equation in the form y = mx + b and determine the slope.

Step-by-step explanation:

To find the slopes of the constraint boundary lines, we need to rearrange each constraint equation in the form y = mx + b, where m is the slope.

1. For constraint (1):

   10X1 + 8X2 = 40

   8X2 = -10X1 + 40

   X2 = -1.25X1 + 5

   The slope of this equation is -1.25.

2. For constraint (2):

   X1 + 4X2 = 8

   4X2 = -X1 + 8

   X2 = -0.25X1 + 2

   The slope of this equation is -0.25.