Question 106606
Product x: Each item sold produces $100 profit
Labor cost: is 3 hours for assembly, 1 hour in detail work, and 2 hours for QA & packing product. 
Product y: Each item sold produces $150 profit
Labor cost: is 5 hours for assembly, 3 hour in detail work, and 2 hours for QA & packing product. 
Company has these hours available for production for each accounting period:
3900 hours for assembly, 2100 hours for detail work, & 2200 hours for QA & packing. 
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Profit function: Profit = 100x + 150y
Assembly : 3x+5y<=3900
Detail   : x +3y<=2100
QA&Pack  : 2x+2y<=2200
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Questions are:
1) How many products of both x & y should be produced to make a max & min profit?
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You have to develop a solution set for the Assembly/Detail/QA&Pack inequalities
Then you have to determine the coordinates of the vertices of this solution 
set.
Then you have to substitute the x/y values of each of these vertices into
the Profit function to see where you get a maximum profit and where you get
a minimum profit.
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2) Now what if product y profit goes up to $170 each. How many products are needed to make a max & min profit? 
The only thing that will change is the Profit function; it will become
Profit = 100x + 170y
To find the man or min you follow the same procedure you did with the 
former Profit equation.
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This whole procedure is called linear programming.
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Cheers,
Stan H.