A student has $500. She buys pencil at $50 each and erasers at $20 each. '
Very expensive pencils and erasers!!!
Let x = the number of pencils.
Let y = the number of erasers. Then:
Money spent on pencils = 50x
Money spent on erasers = 20y
So which simplifies to
She gets at least 5 of each
So and
and the money spent on pencils is over $100 more that that spend on erasers.
So which simplifies to
The system of inequalities is:
We graph the 5 lines, the second one dotted, the others solid:
The feasible region is the quadrilateral below. Since the number
of pencils and erasers must be whole numbers, we circle all the
points with whole numbers for both coordinates (called "lattice
points"). We include all the lattice points which are on any of
the sides of the quadrilateral which are solid, but not on the
side which is dotted. [Note: We cannot include (6,10) because
even though it is on a side which is solid, it is also on the
side which is dotted.
Find:
a. How many ways the money can be spent?
These are represented by the circled points in or on the
feasible region (inside the quadrilateral or on the
quadrilateral's solid sides but not on the dotted side):
We count the circled points and find there are 12 of them.
(x=no. of pencils, y=no. of erasers):
(5,5), (5,6), (5,7), (6,5), (6,6), (6,7),
(6,8), (6,9), (7,5), (7,6), (7,7), (8,5).
b. The greatest number of pencils that can be bought.
That's the greatest x-coordinate, which is 8.
c. The greatest number of erasers that can be bought.
That's the greatest y-coordinate, which is 9.
Edwin