Class notes 9-14 page 21 items 2, 3, 4, 5

Let x = the number of games made at plant 1,
Let y = the number of games made at plant 2.

In the columns of the table, write "times x" next to the numbers in the plant 1 column and write "times y" next to the numbers in the plant 2 column.

The rows of the table give the information needed to write the constraints:  There are only 1700, 1800, and 2400 hours available in the given rows of motherboard production, technical labor, and general manufacturing.
9x + 1y < or = 1700
9x + 3y < or = 1800
4x + 8y < or = 2400
These constraint expressions tell us how much of the resources we can USE.

We want to get as much as we can but we are limited in what we can use.

Graph the constraints using easy points (0,y) and (x,0)

9x + 1y < or = 1700        gives points at ( 0, 1700 ) and ( 188, 0 )

9x + 3y < or = 1800        gives points at ( 0, 600 ) and ( 200, 0 )

4x + 8y < or = 2400        gives points at ( 0, 300 ) and ( 600, 0 )


These lines form a polygonal feasible region.  The vertices (corners) interest us because one of them may give a maximum value for the profit objective function.

The profit objective function is P = 90x + 70y.  This expresses what we want to GET.

In class we estimated that one of the vertices was at (120, 240).  When we plug these quantities of gaming systems into the profit objective function, we get 90(150) + 70(250) = $27,600.

We tried another vertex ( 0, 300 ) in the profit objective function, getting 90(0) + 70(300) = $21,000.

We make more money at the point (120, 240), meaning we should make 120 games at plant 1 and 240 games at plant 2.

Try two other vertices to see if their coordinates give a higher profit.