Use the red equation in a system with the green equation
4x + 8y = 2400 and
9x + 3y = 1800
Hint - make the equations simpler; divide the 1st equation by 4
x + 2y = 600
and divide the second equation by 3.
3x + y = 600
Then use an "x =" or a "y =" to substitute, for example
x = 600 - 2y
make x tmporarily go away
3(600 - 2y) + y = 600 by substituting for x next to the 3
1800 - 6y + y = 600 by distribution
1800 - 5y = 600 by combining "y" terms
-5y = -1200 by subtracting 1800 from each side
y = 240 by dividing by -5 on each side
bring back x
x = 600 - 2(240) by substituting for y in the earlier equation
x = 600 - 480
x = 120
the solution (x,y) where these graphs intersect is (120, 240)
(120, 240) is a vertex for the feasible region
Solve for the coordinates of the vertex where green crosses blue
Use the green equation in a system with the blue equation
9x + 3y = 1800 and
9x + y = 1700
Hint - use a "y = " equation to substitute
y = 1700 - 9x by subtracting 9x from each side
make y go away temporarily
9x + 3(1700 - 9x) = 1800 by substituting for y next to the 3
9x + 5100 - 27x = 1800 by distributing
-18x + 5100 = 1800 by combining "x" terms
-18x = -3300 by subtracting 5100 from each side
x = 183 by dividing each side by -18
bring back y
9(183) + y = 1700 by substituting 183 for x next to the 9 in the earlier equation
1647 + y = 1700 by multiplying
y = 53 by subtracting 1647 from both sides
the solution (x,y) where these graphs intersect is (183, 53)
(183, 53) is a vertex for the feasible region
The calculated vertices for the feasible region are (0,0), (0, 300), (120, 240), (183, 53) and (200,)
These are the combinations of the numbers of games made at plant 1 and plant 2 that you will use to test in the objective function P = 90x + 70y.
Plug in all five ordered pairs and see which one gives you a maximum value for P.
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