Question

3. Minimize P = 3x – 25y + 38 given the following constraints: y+ -44 144 - 98 < 70 12y - 6x > -36 > -6 The minimum is: at (​

Answer 1

-118 at (-2, 6)

Explanation:

See the attached image of the graph! I used a piece of graph paper (and a ruler!) at first, because the graphing program I used was hard to follow in all the shading! The "feasible region" -- I'm assuming this is a linear programming problem is inside an irregular hexagon. I put big red dots on the corner points. Those points are:

(2, 2), (-2, 6), (-6, 4), (-6, -1), (-2, -4), (2, -2)

Plug these coordinates into the expression P = 3x - 25y + 38 to get a value at each of the corner points. Pick out the smallest value.

See the other attached image for those values.

Careful graphing is essential!