Question 322801: Billy Penny is trying to determine how many units of two types of lawn mowers to produce each day. One of these is the standard model, while the other is the deluxe model. The profit per unit on the standard model is $60, while the profit per unit on the deluxe model is $40. The standard model requires 20 minutes of assembly time, while the deluxe model requires 35 minutes of assembly time. The standard model requires 10 minutes of inspection time, while the delux model requires 15 minutes of inspection time. The company must fill an order for 6 deluxe models. There are 450 minutes of assembly time and 180 minutes of inspection time available each day. How many units of each product should be manufactured to maximize profits?
x= number of standard units to produce
y= number of deluxe units to produce
Maximize
Subject to:
My answer:
x y
Stan. Mod. Del. Model Avail. hours
Assembly Time 20 10 450
Inspection Time 35 15 180
Profit $60 $40
Maximize - 60X + 15Y
Subject to - 20x + 35y <= 450
10x + 15y <= 240
y<=6
then I get lost
Answer by Fombitz(32388)   (Show Source):
You can put this solution on YOUR website! x-number of standard units
y-number of deluxe units
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Maximize profits-  <--- Yes!
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 <--- Yes, assembly time bound
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 <--- No, not 240, 180
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 <--- No, "The company must fill an order for 6 deluxe models" so at least  .
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OK, graph all of the bounds and show the feasible region.
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Find the intersection points of axes and the green line, the bounding lines do not intersect each other so only the green line will be used 
(9,6)
(0,12)
(0,6)
The maximum and minimum for the function occurs at the vertices of the feasible region.
Calculate the value at each point.
(9,6):
(0,12):
(0,6):
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To maximize profits at $588, make 9 standard models and 6 deluxe models per day.
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