Question 1189435
let x = the number of TV
let y = the number of DVD


the commission on the sale of TV = .04 * 650 * x.
the commission on the sale of DVD = .09 * 225 * y.


your inequality is .04 * 650 * x + .09 * 225 * y >= 1800


simplify to get:


y >= 26 * x + 20.25 * Y >= 1800.


any integral point on or above this line will satisfy the inequality.


here's what the graph of the equation of that line looks like.


<img src = "http://theo.x10hosting.com/2022/011203.jpg" >


critical points are (0,59.259) and (46.154,0).
if an integer value of y is greater than 59.259, then any positive integer value of x is good.
if an integer value of x is greater than 46.154, then any positive integer value of y is good.


for example, if you evaluate the inequality at each of the coordinate points shown, you will get:


at (0,60), you get 26 * 0 + 20.25 * 60 = 1215 which is greater than 1200.
at (47,0), you get 26 * 47 + 20.25 * 0 = 1222 which is greater than 1200.
at (10,10), you get 26 * 10 + 20.25 * 10 = 462.5 which is NOT greater than 1200.
at (40,40), you get 26 * 40 + 20.25 * 40 = 1850 which is greater than 1200.


the value of both x and y must be greater than or eual to 0, because the number of TV or DVD can't be negative.