Answer:
Maximum (250,125) Answer
Explanation:
This is more of a graphing problem than it is anything else.
Begin by graphing all 4 given equations.
When you do that, mark the intersection points of at least 2 lines. In this case it is exactly 2 lines for each intersecting point.
6x + 4y <= 2000 and 2x + 4y <= 1000 intersect at (250,125)
x=>0 and y=>0 intersect at (0,0)
6x + 4y <=2000 and x => 0 intersect at 333.333
2x + 4y <=1000 and y>=0 intersect at 0,250.
Any other intersection points fall outside the range of the givens. The shaded part we are interested in is sort of a very dark green/blue. It is the interior of the quadrilateral determined by the 4 vertices that are marked.
Now all you have to do is determine the maximum point using P=15x + 12y
For 0,0 P = 15*0 + 12,0 = 0
For 0,250 P = 15*0 + 12*250 = 3000
For 333.3333,0 P = 15*333.3333 + 12*0 = 5000 rounded.
For 250,125 P = 15*250 + 12*125 = 5250 Which is the maximum
Answer (250,125) produces the maximum value Answer