SOLUTION: Math word problem The Amazon website plans to purchase ads in a local newspaper advertising their site. Their operating budget will allow them to spend at most $2200 on this ad

Question 1027282: Math word problem
The Amazon website plans to purchase ads in a local newspaper advertising their site. Their operating budget will allow them to spend at most $2200 on this advertising adventure. They plan to run at most 20 ads. An ad will cost $50 to appear in the weekday paper and $200 to appear in a weekend edition. Prepare a graph that will represent all of the possible combinations of ads under these conditions.
How can I create a system of inequalities to represent this data?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
let x equal the number of ads during the week.
let y equal the number of ads during the weekend.

your constraint equations are:

x + y <= 20

50x + 200y <= 2200

x >= 0

y > = 0

you would graph the equality portion of these equations after solving them for y.

x + y <= 20 becomes y <= 20 - x
you would graph y = 20 - x

50x + 200y <= 2200 becomes y <= (2200-50x)/200
you would graph y = (2200-50x)/200

x = 0 is a vertical line at x = 0.
it's actually the y-axis.

y = 0 is a horizontal line as y = 0.
it's actually the x-axis.

your feasible is the area on the graph that is on or below the line y = 20-x; on or below the line y = (2200-50x)/200; on or above the line y = 0; on or to the right of the line x = 0.

the graph is shown below:

$$$

any point on the lines or below the lines and to the right of y = 0 and above x = 0 are valid points.

those are all the possible combinations that would satisfy the requirements.

for example:

at the point (12,8):

x + y = 20 which satisfies the criteria that the number of ads is less than or equal to 20.

50x + 100y = 50*12 + 200*8 = 600 + 1600 = 2200 which satisfies the criteria that the total price of the ads is less than or equal to 2200 dollars.

as another example, any point within the area enclosed by those lines would also satisfy the criteria.

for example, the point (5,5) is in that area and satisfies the criteria.

x+y = 10 which is less than 20.

50*5 + 200*5 = 250 + 1000 = 1250 which is less than 2200.

the enclosed area is called the feasible region.

the corner points of the feasible region contain the max/min values of the objective function, if you had one.

you don't in this graph because all that was required was for you to graph the constraints.

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