solve the linear programming

Question

Maximize

P=30x+40y

Subject to 2x+y <_ 16

x+y <_ 9

x+2y <_ 14

x,y >_ 0

Answer 1

The critical points are:

(0,7) ---> p(0,7) = 280

(4,5) ---> p(4,5) = 120+200 = 320

(7,2) ---> p(7,2) = 30*7 + 40*2 = 210 + 80 = 290

(8,0) --- > p(8,0) = 240

(4,5) maximizes

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intersection points:

2x+y = 16

x + y = 9

---------------- <-- subtracting them

x = 7 --> (7,2)

2x+y = 16

x + 2y = 14

multiplies bottom equation by 2

2x +y = 16

2x + 4y = 28

3y = 12

y = 4

x=6

(6,4) --> not in the solution set...

x+y=9

x+2y=14

y=5

x=4 (4,5)