SOLUTION: Jill sells TVs and DVD players. She earns 4% commission on each tv and 9% commission on each DVD player. The price of tv is $650 and the price of a DVD player is $225. She wants to

Question 1189435: Jill sells TVs and DVD players. She earns 4% commission on each tv and 9% commission on each DVD player. The price of tv is $650 and the price of a DVD player is $225. She wants to earn a minimum of $1200 commission each month.
a) Write an inequality that represents this situation.
b) Sketch the inequality, showing all key points
State a potential solution to the problem
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
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.

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.

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