Graphing and Statistics

Question

Minimize	z=2x+y
Subject to	3y+5x≥27 5y+3x≥27 y+x≥7 x≥0 y≥0

Minimum is   ________________ at

x =   _________

y = __________

Answer 1

this is a linear programming program

solve by graphing the inequalities

then check each corner ordered pair with the objective function, z=2x+y to find the min value of z

should be the lower left corner of the triangle where x=y=3.5

5x+3y>/=27

3x+5y>/=27

x+y>/=7

other two constraints eliminate all but the 1st quadrant

(3.5,3.5)

z = 10.5