Maximize and Minimize P5x9y subject to x90SolutionLets check

Maximize and Minimize

P=5x+9y

subject to

x+9<2

x+3y<4

4x+5x>20

x,y>0

Solution

Let\'s check the conditions first.

x+9<2 implies x < -7. This is not true as x > 0 given.

4x + 5x > 20 implies x > 20/9 > 2.22

x+3y < 4 implies y< 4-x/3 --------- (1)

if we put x=3 in (1) we get, y < 1/3

P= 4x+5y = 4*3 + 9*1/3 = 15 can be minimum value.

If we put x equal to 4, we get y = 0.

P = 4*4 = 16