Question 216840: Linear programming solve and graph
Lumber Company can convert logs into either Lumber or plywood. In a given week the mill can turn out 400 units of production, of which 100 units of lumber and 150 units of plywood are required by regular customers. The profit on a unit of lumber is $20 and on a unit of plywood is $30. How many units of each type should the mill produce in order to maximize profit.
I'm looking for an answer on how to do the calculations, step by step, and not just a fast answer.
Thanks
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Lumber Company can convert logs into either Lumber or plywood. In a given week the mill can turn out 400 units of production, of which 100 units of lumber and 150 units of plywood are required by regular customers. The profit on a unit of lumber is $20 and on a unit of plywood is $30. How many units of each type should the mill produce in order to maximize profit.
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L >= 0
P >= 0
L + P = 400
Lumber Inequality: 100 <= L <=400
Plywood Inequality: 150<= P <= 400
Objective Function: Profit = 20L + 30P
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Let the horizontal axis be "L"; Let the vertical axis be "P"
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Draw vertical lines at L = 100 and at L = 400
Draw horizontal lines at P = 150 and at P = 400
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Graph the line P = -L+400
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Find the intersection points and check there coordinates
in the Objective Function to see which pair gives the
maximum profit.
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Cheers,
Stan H.
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